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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Se connectar</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pàgines per a editors no registrats <a href="/wiki/Ajuda:Introducci%C3%B3" aria-label="Vegeu més informació sobre l'edició"><span>més informació</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Especial:Mas_contribucions" title="Una llista de les modificacions fetes des d'aquesta adreça IP [y]" accesskey="y"><span>Contribucions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Mas_discussions" title="La pagina de discussion per aquesta adreça IP [n]" accesskey="n"><span>Discussion</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Somari" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Somari</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mòu a la barra laterala</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">Escondre</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Començament</div> </a> </li> <li id="toc-Istòria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Istòria"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Istòria</span> </div> </a> <ul id="toc-Istòria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tipes_principals_d'eqüacions_diferenciali" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tipes_principals_d'eqüacions_diferenciali"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tipes principals d'eqüacions diferenciali</span> </div> </a> <button aria-controls="toc-Tipes_principals_d'eqüacions_diferenciali-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Tipes principals d'eqüacions diferenciali</span> </button> <ul id="toc-Tipes_principals_d'eqüacions_diferenciali-sublist" class="vector-toc-list"> <li id="toc-Li_eqüacions_diferenciali_ordinari" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Li_eqüacions_diferenciali_ordinari"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Li eqüacions diferenciali ordinari</span> </div> </a> <ul id="toc-Li_eqüacions_diferenciali_ordinari-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Li_eqüacions_diferenciali_parciali" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Li_eqüacions_diferenciali_parciali"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Li eqüacions diferenciali parciali</span> </div> </a> <ul id="toc-Li_eqüacions_diferenciali_parciali-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Li_eqüacions_diferenciali_non_lineari" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Li_eqüacions_diferenciali_non_lineari"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Li eqüacions diferenciali non lineari</span> </div> </a> <ul id="toc-Li_eqüacions_diferenciali_non_lineari-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Resolucion_dei_eqüacions_diferenciali" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Resolucion_dei_eqüacions_diferenciali"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Resolucion dei eqüacions diferenciali</span> </div> </a> <button aria-controls="toc-Resolucion_dei_eqüacions_diferenciali-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Resolucion dei eqüacions diferenciali</span> </button> <ul id="toc-Resolucion_dei_eqüacions_diferenciali-sublist" class="vector-toc-list"> <li id="toc-Existéncia_de_solucions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Existéncia_de_solucions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Existéncia de solucions</span> </div> </a> <ul id="toc-Existéncia_de_solucions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quaucu_cas_simples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quaucu_cas_simples"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Quaucu cas simples</span> </div> </a> <ul id="toc-Quaucu_cas_simples-sublist" class="vector-toc-list"> <li id="toc-Eqüacions_diferenciali_ordinari_dau_promier_gra" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Eqüacions_diferenciali_ordinari_dau_promier_gra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Eqüacions diferenciali ordinari dau promier gra</span> </div> </a> <ul id="toc-Eqüacions_diferenciali_ordinari_dau_promier_gra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eqüacions_diferenciali_ordinari_dau_segond_gra" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Eqüacions_diferenciali_ordinari_dau_segond_gra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>Eqüacions diferenciali ordinari dau segond gra</span> </div> </a> <ul id="toc-Eqüacions_diferenciali_ordinari_dau_segond_gra-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Aplicacions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplicacions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Aplicacions</span> </div> </a> <ul id="toc-Aplicacions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Annèxas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Annèxas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Annèxas</span> </div> </a> <button aria-controls="toc-Annèxas-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Annèxas</span> </button> <ul id="toc-Annèxas-sublist" class="vector-toc-list"> <li id="toc-Ligams_intèrnes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ligams_intèrnes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Ligams intèrnes</span> </div> </a> <ul id="toc-Ligams_intèrnes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nòtas_e_referéncias" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nòtas_e_referéncias"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Nòtas e referéncias</span> </div> </a> <ul id="toc-Nòtas_e_referéncias-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Somari" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Commuta la taula de continguts." > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Commuta la taula de continguts.</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Equacion diferenciala</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Vés a un article en una altra llengua. Disponible en 95 llengües" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-95" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">95 lengas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Differensiaalvergelyking" title="Differensiaalvergelyking - afrikaans" lang="af" hreflang="af" data-title="Differensiaalvergelyking" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Differentialgleichung" title="Differentialgleichung - aleman de Soïssa" lang="gsw" hreflang="gsw" data-title="Differentialgleichung" data-language-autonym="Alemannisch" data-language-local-name="aleman de Soïssa" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Ecuaci%C3%B3n_diferencial" title="Ecuación diferencial - aragonés" lang="an" hreflang="an" data-title="Ecuación diferencial" data-language-autonym="Aragonés" data-language-local-name="aragonés" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D8%AA%D9%81%D8%A7%D8%B6%D9%84%D9%8A%D8%A9" title="معادلة تفاضلية - arabi" lang="ar" hreflang="ar" data-title="معادلة تفاضلية" data-language-autonym="العربية" data-language-local-name="arabi" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Ecuaci%C3%B3n_diferencial" title="Ecuación diferencial - asturian" lang="ast" hreflang="ast" data-title="Ecuación diferencial" data-language-autonym="Asturianu" data-language-local-name="asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Diferensial_t%C9%99nlikl%C9%99r" title="Diferensial tənliklər - azerbaijani" lang="az" hreflang="az" data-title="Diferensial tənliklər" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C_%D1%82%D0%B8%D0%B3%D0%B5%D2%99%D0%BB%D3%99%D0%BC%D3%99" title="Дифференциаль тигеҙләмә - baixkir" lang="ba" hreflang="ba" data-title="Дифференциаль тигеҙләмә" data-language-autonym="Башҡортса" data-language-local-name="baixkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%8B%D1%84%D0%B5%D1%80%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D0%B5_%D1%9E%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5" title="Дыферэнцыяльнае ўраўненне - belarús" lang="be" hreflang="be" data-title="Дыферэнцыяльнае ўраўненне" data-language-autonym="Беларуская" data-language-local-name="belarús" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%94%D1%8B%D1%84%D1%8D%D1%80%D1%8D%D0%BD%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D0%B5_%D1%80%D0%B0%D1%9E%D0%BD%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Дыфэрэнцыйнае раўнаньне - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Дыфэрэнцыйнае раўнаньне" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%BE_%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5" title="Диференциално уравнение - bulgar" lang="bg" hreflang="bg" data-title="Диференциално уравнение" data-language-autonym="Български" data-language-local-name="bulgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%AC%E0%A6%95%E0%A6%B2%E0%A6%A8%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%B8%E0%A6%AE%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3" title="ব্যবকলনীয় সমীকরণ - bengalin" lang="bn" hreflang="bn" data-title="ব্যবকলনীয় সমীকরণ" data-language-autonym="বাংলা" data-language-local-name="bengalin" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Diferencijalna_jedna%C4%8Dina" title="Diferencijalna jednačina - bosniac" lang="bs" hreflang="bs" data-title="Diferencijalna jednačina" data-language-autonym="Bosanski" data-language-local-name="bosniac" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Equaci%C3%B3_diferencial" title="Equació diferencial - catalan" lang="ca" hreflang="ca" data-title="Equació diferencial" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%BE%D8%A7%D9%88%DA%A9%DB%8E%D8%B4%DB%95%DB%8C_%D8%AC%DB%8C%D8%A7%DA%A9%D8%A7%D8%B1%DB%8C" title="ھاوکێشەی جیاکاری - kurd central" lang="ckb" hreflang="ckb" data-title="ھاوکێشەی جیاکاری" data-language-autonym="کوردی" data-language-local-name="kurd central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Diferenci%C3%A1ln%C3%AD_rovnice" title="Diferenciální rovnice - chèc" lang="cs" hreflang="cs" data-title="Diferenciální rovnice" data-language-autonym="Čeština" data-language-local-name="chèc" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BB%C4%83_%D1%82%D0%B0%D0%BD%D0%BB%C4%83%D1%85" title="Дифференциаллă танлăх - chovash" lang="cv" hreflang="cv" data-title="Дифференциаллă танлăх" data-language-autonym="Чӑвашла" data-language-local-name="chovash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Hafaliad_differol" title="Hafaliad differol - gal·lès" lang="cy" hreflang="cy" data-title="Hafaliad differol" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Differentialligning" title="Differentialligning - danés" lang="da" hreflang="da" data-title="Differentialligning" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Differentialgleichung" title="Differentialgleichung - alemand" lang="de" hreflang="de" data-title="Differentialgleichung" data-language-autonym="Deutsch" data-language-local-name="alemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CF%86%CE%BF%CF%81%CE%B9%CE%BA%CE%AE_%CE%B5%CE%BE%CE%AF%CF%83%CF%89%CF%83%CE%B7" title="Διαφορική εξίσωση - grèc" lang="el" hreflang="el" data-title="Διαφορική εξίσωση" data-language-autonym="Ελληνικά" data-language-local-name="grèc" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Differential_equation" title="Differential equation - anglés" lang="en" hreflang="en" data-title="Differential equation" data-language-autonym="English" data-language-local-name="anglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Diferenciala_ekvacio" title="Diferenciala ekvacio - esperanto" lang="eo" hreflang="eo" data-title="Diferenciala ekvacio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ecuaci%C3%B3n_diferencial" title="Ecuación diferencial - espanhòl" lang="es" hreflang="es" data-title="Ecuación diferencial" data-language-autonym="Español" data-language-local-name="espanhòl" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Diferentsiaalv%C3%B5rrand" title="Diferentsiaalvõrrand - estonian" lang="et" hreflang="et" data-title="Diferentsiaalvõrrand" data-language-autonym="Eesti" data-language-local-name="estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ekuazio_diferentzial" title="Ekuazio diferentzial - basc" lang="eu" hreflang="eu" data-title="Ekuazio diferentzial" data-language-autonym="Euskara" data-language-local-name="basc" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D9%87_%D8%AF%DB%8C%D9%81%D8%B1%D8%A7%D9%86%D8%B3%DB%8C%D9%84" title="معادله دیفرانسیل - perse" lang="fa" hreflang="fa" data-title="معادله دیفرانسیل" data-language-autonym="فارسی" data-language-local-name="perse" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Differentiaaliyht%C3%A4l%C3%B6" title="Differentiaaliyhtälö - finlandés" lang="fi" hreflang="fi" data-title="Differentiaaliyhtälö" data-language-autonym="Suomi" data-language-local-name="finlandés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89quation_diff%C3%A9rentielle" title="Équation différentielle - francés" lang="fr" hreflang="fr" data-title="Équation différentielle" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Cothrom%C3%B3id_dhifre%C3%A1lach" title="Cothromóid dhifreálach - irlandés" lang="ga" hreflang="ga" data-title="Cothromóid dhifreálach" data-language-autonym="Gaeilge" data-language-local-name="irlandés" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程 - xinès gan" lang="gan" hreflang="gan" data-title="微分方程" data-language-autonym="贛語" data-language-local-name="xinès gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Ecuaci%C3%B3n_diferencial" title="Ecuación diferencial - galician" lang="gl" hreflang="gl" data-title="Ecuación diferencial" data-language-autonym="Galego" data-language-local-name="galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%94_%D7%93%D7%99%D7%A4%D7%A8%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA" title="משוואה דיפרנציאלית - ebrèu" lang="he" hreflang="he" data-title="משוואה דיפרנציאלית" data-language-autonym="עברית" data-language-local-name="ebrèu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%B5%E0%A4%95%E0%A4%B2_%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3" title="अवकल समीकरण - Indi" lang="hi" hreflang="hi" data-title="अवकल समीकरण" data-language-autonym="हिन्दी" data-language-local-name="Indi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Differential_equation" title="Differential equation - hindi de Fiji" lang="hif" hreflang="hif" data-title="Differential equation" data-language-autonym="Fiji Hindi" data-language-local-name="hindi de Fiji" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Diferencijalne_jednad%C5%BEbe" title="Diferencijalne jednadžbe - croat" lang="hr" hreflang="hr" data-title="Diferencijalne jednadžbe" data-language-autonym="Hrvatski" data-language-local-name="croat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Differenci%C3%A1legyenlet" title="Differenciálegyenlet - ongrés" lang="hu" hreflang="hu" data-title="Differenciálegyenlet" data-language-autonym="Magyar" data-language-local-name="ongrés" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%AB%D6%86%D5%A5%D6%80%D5%A5%D5%B6%D6%81%D5%AB%D5%A1%D5%AC_%D5%B0%D5%A1%D5%BE%D5%A1%D5%BD%D5%A1%D6%80%D5%B8%D6%82%D5%B4%D5%B6%D5%A5%D6%80" title="Դիֆերենցիալ հավասարումներ - armèni" lang="hy" hreflang="hy" data-title="Դիֆերենցիալ հավասարումներ" data-language-autonym="Հայերեն" data-language-local-name="armèni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%8F%D5%A1%D6%80%D5%A2%D5%A5%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B0%D5%A1%D6%82%D5%A1%D5%BD%D5%A1%D6%80%D5%B8%D6%82%D5%B4%D5%B6%D5%A5%D6%80" title="Տարբերական հաւասարումներ - arménien occidental" lang="hyw" hreflang="hyw" data-title="Տարբերական հաւասարումներ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="arménien occidental" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Persamaan_diferensial" title="Persamaan diferensial - indonesian" lang="id" hreflang="id" data-title="Persamaan diferensial" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Diffurjafna" title="Diffurjafna - islandés" lang="is" hreflang="is" data-title="Diffurjafna" data-language-autonym="Íslenska" data-language-local-name="islandés" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Equazione_differenziale" title="Equazione differenziale - italian" lang="it" hreflang="it" data-title="Equazione differenziale" data-language-autonym="Italiano" data-language-local-name="italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%BC%8F" title="微分方程式 - japonés" lang="ja" hreflang="ja" data-title="微分方程式" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Difrenshal_ikwiejan" title="Difrenshal ikwiejan - crioll anglès de Jamaica" lang="jam" hreflang="jam" data-title="Difrenshal ikwiejan" data-language-autonym="Patois" data-language-local-name="crioll anglès de Jamaica" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%98%E1%83%A4%E1%83%94%E1%83%A0%E1%83%94%E1%83%9C%E1%83%AA%E1%83%98%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%92%E1%83%90%E1%83%9C%E1%83%A2%E1%83%9D%E1%83%9A%E1%83%94%E1%83%91%E1%83%94%E1%83%91%E1%83%98" title="დიფერენციალური განტოლებები - georgian" lang="ka" hreflang="ka" data-title="დიფერენციალური განტოლებები" data-language-autonym="ქართული" data-language-local-name="georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Differensial_te%C5%84leme" title="Differensial teńleme - karakalpak" lang="kaa" hreflang="kaa" data-title="Differensial teńleme" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D1%82%D0%B5%D2%A3%D0%B4%D0%B5%D1%83" title="Дифференциалдық теңдеу - cazac" lang="kk" hreflang="kk" data-title="Дифференциалдық теңдеу" data-language-autonym="Қазақша" data-language-local-name="cazac" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9F%E1%9E%98%E1%9E%B8%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%8C%E1%9E%B8%E1%9E%95%E1%9F%81%E1%9E%9A%E1%9F%89%E1%9E%84%E1%9F%8B%E1%9E%9F%E1%9F%92%E1%9E%99%E1%9F%82%E1%9E%9B" title="សមីការឌីផេរ៉ង់ស្យែល - cambojian" lang="km" hreflang="km" data-title="សមីការឌីផេរ៉ង់ស្យែល" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="cambojian" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AF%B8%EB%B6%84%EB%B0%A9%EC%A0%95%EC%8B%9D" title="미분방정식 - corean" lang="ko" hreflang="ko" data-title="미분방정식" data-language-autonym="한국어" data-language-local-name="corean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hevk%C3%AA%C5%9Feya_d%C3%AEferensiyel" title="Hevkêşeya dîferensiyel - curd" lang="ku" hreflang="ku" data-title="Hevkêşeya dîferensiyel" data-language-autonym="Kurdî" data-language-local-name="curd" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Aequatio_differentialis" title="Aequatio differentialis - latin" lang="la" hreflang="la" data-title="Aequatio differentialis" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D0%B1%D0%B0%D1%80%D0%B0%D0%B1%D0%B0%D1%80%D0%B2%D0%B0%D0%BB" title="Дифференциал барабарвал - lesguià" lang="lez" hreflang="lez" data-title="Дифференциал барабарвал" data-language-autonym="Лезги" data-language-local-name="lesguià" class="interlanguage-link-target"><span>Лезги</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Equazzion_diferenziala" title="Equazzion diferenziala - llombard" lang="lmo" hreflang="lmo" data-title="Equazzion diferenziala" data-language-autonym="Lombard" data-language-local-name="llombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Diferencialin%C4%97_lygtis" title="Diferencialinė lygtis - lituan" lang="lt" hreflang="lt" data-title="Diferencialinė lygtis" data-language-autonym="Lietuvių" data-language-local-name="lituan" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Diferenci%C4%81lvien%C4%81dojums" title="Diferenciālvienādojums - leton" lang="lv" hreflang="lv" data-title="Diferenciālvienādojums" data-language-autonym="Latviešu" data-language-local-name="leton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%80%D0%B0%D0%B2%D0%B5%D0%BD%D0%BA%D0%B0" title="Диференцијална равенка - macedonian" lang="mk" hreflang="mk" data-title="Диференцијална равенка" data-language-autonym="Македонски" data-language-local-name="macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%B5%E0%B4%95%E0%B4%B2%E0%B4%B8%E0%B4%AE%E0%B4%B5%E0%B4%BE%E0%B4%95%E0%B5%8D%E0%B4%AF%E0%B4%82" title="അവകലസമവാക്യം - malaiàlam" lang="ml" hreflang="ml" data-title="അവകലസമവാക്യം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Persamaan_pembezaan" title="Persamaan pembezaan - malai" lang="ms" hreflang="ms" data-title="Persamaan pembezaan" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Ekwazzjoni_differenzjali" title="Ekwazzjoni differenzjali - maltés" lang="mt" hreflang="mt" data-title="Ekwazzjoni differenzjali" data-language-autonym="Malti" data-language-local-name="maltés" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Differentiaalvergelijking" title="Differentiaalvergelijking - neerlandés" lang="nl" hreflang="nl" data-title="Differentiaalvergelijking" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Differensiallikning" title="Differensiallikning - norvegian nynorsk" lang="nn" hreflang="nn" data-title="Differensiallikning" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegian nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Differensialligning" title="Differensialligning - norvegian bokmål" lang="nb" hreflang="nb" data-title="Differensialligning" data-language-autonym="Norsk bokmål" data-language-local-name="norvegian bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A1%E0%A8%BF%E0%A8%AB%E0%A8%BC%E0%A8%B0%E0%A9%88%E0%A8%82%E0%A8%B8%E0%A8%BC%E0%A9%80%E0%A8%85%E0%A8%B2_%E0%A8%B8%E0%A8%AE%E0%A9%80%E0%A8%95%E0%A8%B0%E0%A8%A8" title="ਡਿਫ਼ਰੈਂਸ਼ੀਅਲ ਸਮੀਕਰਨ - punjabi" lang="pa" hreflang="pa" data-title="ਡਿਫ਼ਰੈਂਸ਼ੀਅਲ ਸਮੀਕਰਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/R%C3%B3wnanie_r%C3%B3%C5%BCniczkowe" title="Równanie różniczkowe - polonés" lang="pl" hreflang="pl" data-title="Równanie różniczkowe" data-language-autonym="Polski" data-language-local-name="polonés" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Equassion_diferensial" title="Equassion diferensial - piemontès" lang="pms" hreflang="pms" data-title="Equassion diferensial" data-language-autonym="Piemontèis" data-language-local-name="piemontès" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AA%D9%81%D8%B1%DB%8C%D9%82%DB%8C_%D9%85%D8%B3%D8%A7%D9%88%D8%A7%D8%AA" title="تفریقی مساوات - Western Punjabi" lang="pnb" hreflang="pnb" data-title="تفریقی مساوات" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Equa%C3%A7%C3%A3o_diferencial" title="Equação diferencial - portugués" lang="pt" hreflang="pt" data-title="Equação diferencial" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ecua%C8%9Bie_diferen%C8%9Bial%C4%83" title="Ecuație diferențială - romanés" lang="ro" hreflang="ro" data-title="Ecuație diferențială" data-language-autonym="Română" data-language-local-name="romanés" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5" title="Дифференциальное уравнение - rus" lang="ru" hreflang="ru" data-title="Дифференциальное уравнение" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Equazzioni_diffirinziali" title="Equazzioni diffirinziali - sicilian" lang="scn" hreflang="scn" data-title="Equazzioni diffirinziali" data-language-autonym="Sicilianu" data-language-local-name="sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Differential_equation" title="Differential equation - escossés" lang="sco" hreflang="sco" data-title="Differential equation" data-language-autonym="Scots" data-language-local-name="escossés" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Diferencijalna_jedna%C4%8Dina" title="Diferencijalna jednačina - serbocroat" lang="sh" hreflang="sh" data-title="Diferencijalna jednačina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B7%80%E0%B6%9A%E0%B6%BD_%E0%B7%83%E0%B6%B8%E0%B7%93%E0%B6%9A%E0%B6%BB%E0%B6%AB%E0%B6%BA" title="අවකල සමීකරණය - singalès" lang="si" hreflang="si" data-title="අවකල සමීකරණය" data-language-autonym="සිංහල" data-language-local-name="singalès" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Differential_equation" title="Differential equation - Simple English" lang="en-simple" hreflang="en-simple" data-title="Differential equation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Diferenci%C3%A1lna_rovnica" title="Diferenciálna rovnica - eslovac" lang="sk" hreflang="sk" data-title="Diferenciálna rovnica" data-language-autonym="Slovenčina" data-language-local-name="eslovac" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Diferencialna_ena%C4%8Dba" title="Diferencialna enačba - eslovèn" lang="sl" hreflang="sl" data-title="Diferencialna enačba" data-language-autonym="Slovenščina" data-language-local-name="eslovèn" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ekuacionet_diferenciale" title="Ekuacionet diferenciale - albanés" lang="sq" hreflang="sq" data-title="Ekuacionet diferenciale" data-language-autonym="Shqip" data-language-local-name="albanés" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%98%D0%B5%D0%B4%D0%BD%D0%B0%D1%87%D0%B8%D0%BD%D0%B0" title="Диференцијална једначина - serbi" lang="sr" hreflang="sr" data-title="Диференцијална једначина" data-language-autonym="Српски / srpski" data-language-local-name="serbi" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Differentialekvation" title="Differentialekvation - suedés" lang="sv" hreflang="sv" data-title="Differentialekvation" data-language-autonym="Svenska" data-language-local-name="suedés" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Mlinganyo_tenguo" title="Mlinganyo tenguo - swahili" lang="sw" hreflang="sw" data-title="Mlinganyo tenguo" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%95%E0%AF%88%E0%AE%AF%E0%AF%80%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AE%AE%E0%AE%A9%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="வகையீட்டுச் சமன்பாடு - tamol" lang="ta" hreflang="ta" data-title="வகையீட்டுச் சமன்பாடு" data-language-autonym="தமிழ்" data-language-local-name="tamol" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%AD%E0%B8%99%E0%B8%B8%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B9%8C" title="สมการเชิงอนุพันธ์ - tai" lang="th" hreflang="th" data-title="สมการเชิงอนุพันธ์" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Differensial_de%C5%88lemeler" title="Differensial deňlemeler - turcmèn" lang="tk" hreflang="tk" data-title="Differensial deňlemeler" data-language-autonym="Türkmençe" data-language-local-name="turcmèn" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Ekwasyong_diperensiyal" title="Ekwasyong diperensiyal - tagal" lang="tl" hreflang="tl" data-title="Ekwasyong diperensiyal" data-language-autonym="Tagalog" data-language-local-name="tagal" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Diferansiyel_denklem" title="Diferansiyel denklem - turc" lang="tr" hreflang="tr" data-title="Diferansiyel denklem" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D1%96_%D1%80%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D0%BD%D1%8F" title="Диференціальні рівняння - ucrainés" lang="uk" hreflang="uk" data-title="Диференціальні рівняння" data-language-autonym="Українська" data-language-local-name="ucrainés" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%D9%81%D8%B1%D9%82%DB%8C_%D9%85%D8%B3%D8%A7%D9%88%D8%A7%D8%AA" title="تفرقی مساوات - ordó" lang="ur" hreflang="ur" data-title="تفرقی مساوات" data-language-autonym="اردو" data-language-local-name="ordó" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Differensial_tenglama" title="Differensial tenglama - ozbèc" lang="uz" hreflang="uz" data-title="Differensial tenglama" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ozbèc" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Differencialine_tazostuz" title="Differencialine tazostuz - vepse" lang="vep" hreflang="vep" data-title="Differencialine tazostuz" data-language-autonym="Vepsän kel’" data-language-local-name="vepse" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_vi_ph%C3%A2n" title="Phương trình vi phân - vietnamian" lang="vi" hreflang="vi" data-title="Phương trình vi phân" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamian" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Ekwasyon_diferensyal" title="Ekwasyon diferensyal - waray" lang="war" hreflang="war" data-title="Ekwasyon diferensyal" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程 - xinès wu" lang="wuu" hreflang="wuu" data-title="微分方程" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%93%D7%99%D7%A4%D7%A2%D7%A8%D7%A2%D7%A0%D7%A6%D7%99%D7%90%D7%9C-%D7%92%D7%9C%D7%99%D7%99%D7%9B%D7%95%D7%A0%D7%92" title="דיפערענציאל-גלייכונג - yiddish" lang="yi" hreflang="yi" data-title="דיפערענציאל-גלייכונג" data-language-autonym="ייִדיש" data-language-local-name="yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程 - chinés" lang="zh" hreflang="zh" data-title="微分方程" data-language-autonym="中文" data-language-local-name="chinés" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/B%C3%AE-hun_hong-t%C3%AAng-sek" title="Bî-hun hong-têng-sek - xinès min del sud" lang="nan" hreflang="nan" data-title="Bî-hun hong-têng-sek" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="xinès min del sud" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程 - cantonés" lang="yue" hreflang="yue" data-title="微分方程" data-language-autonym="粵語" data-language-local-name="cantonés" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11214#sitelinks-wikipedia" title="Modificar los ligams interlenga" class="wbc-editpage">Modificar los ligams</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espacis de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Equacion_diferenciala" title="Veire l’article [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Discutir:Equacion_diferenciala&action=edit&redlink=1" rel="discussion" class="new" title="Discussion a prepaus d'aquesta pagina (la pagina existís pas) [t]" accesskey="t"><span>Discussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Canvia la variant de llengua" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">occitan</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Afichatges"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Equacion_diferenciala"><span>Legir</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit" title="Modificar aquela pagina [v]" accesskey="v"><span>Modificar</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Equacion_diferenciala&action=edit" title="Modificar lo còdi font d'aquela pagina [e]" accesskey="e"><span>Modificar lo còdi</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Equacion_diferenciala&action=history" title="Los autors e versions precedentas d'aquesta pagina. 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article es redigit en niçard." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Bandi%C3%A8ra_de_Ni%C3%A7a.svg/30px-Bandi%C3%A8ra_de_Ni%C3%A7a.svg.png" decoding="async" width="30" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Bandi%C3%A8ra_de_Ni%C3%A7a.svg/45px-Bandi%C3%A8ra_de_Ni%C3%A7a.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Bandi%C3%A8ra_de_Ni%C3%A7a.svg/60px-Bandi%C3%A8ra_de_Ni%C3%A7a.svg.png 2x" data-file-width="1800" data-file-height="1198" /></a></span></span></div></div> </div> <div id="siteSub" class="noprint">Un article de Wikipèdia, l'enciclopèdia liura.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirigit dempuèi <a href="/w/index.php?title=Eq%C3%BCacion_diferenciala&redirect=no" class="mw-redirect" title="Eqüacion diferenciala">Eqüacion diferenciala</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="oc" dir="ltr"><p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichi%C3%A8r:Exemple_d%27eq%C3%BCacion_diferenciala.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Exemple_d%27eq%C3%BCacion_diferenciala.png/220px-Exemple_d%27eq%C3%BCacion_diferenciala.png" decoding="async" width="220" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Exemple_d%27eq%C3%BCacion_diferenciala.png/330px-Exemple_d%27eq%C3%BCacion_diferenciala.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Exemple_d%27eq%C3%BCacion_diferenciala.png/440px-Exemple_d%27eq%C3%BCacion_diferenciala.png 2x" data-file-width="638" data-file-height="170" /></a><figcaption>Exemple d'eqüacion diferenciala entre una foncion <i>f</i> e la sieua derivada.</figcaption></figure> <p>Una <b>eqüacion diferenciala</b> (var. <b>equacion diferenciala</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>) es una <a href="/wiki/Eq%C3%BCacion" class="mw-redirect" title="Eqüacion">eqüacion</a> que la ò li sieui inconoissudas son de <a href="/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas)">foncions</a> e que se presenta sota la forma d'una relacion entre aqueli foncions e li sieui <a href="/wiki/Derivada" title="Derivada">derivadas</a> successivi. En l'abséncia de precisions particulari, lo tèrme designa generalament li « equäcions diferenciali ordinari » que son caracterizadi per de foncions inconoissudi dependenti d'una variabla unica. Totun, existisse un segond tipe d'eqüacions diferenciali, li eqüacions diferenciali parciali, dont la ò li foncions inconoissudi pòdon dependre de mai d'una variabla. </p><p>Li eqüacions diferenciali an un ròtle important dins li <a href="/wiki/Sci%C3%A9ncia" title="Sciéncia">sciéncias</a> modèrni car aparéisson frequentament dins lu modèles actuaus, especialament en <a href="/wiki/Fisica" title="Fisica">fisica</a>, en <a href="/wiki/Quimia" title="Quimia">quimia</a> e en <a href="/wiki/Biologia" title="Biologia">biologia</a>. En causa d'aquela importància, aqueli eqüacions an fach l'objècte de recèrcas per trobar de metòdes de resolucion sistematica. Aquò es a l'origina d'una classificacion dei eqüacions diferenciali en foncion dau tipe d'eqüacions implicadi dins l'egalitat. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Istòria"><span id="Ist.C3.B2ria"></span>Istòria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=1" title="Modificar la seccion : Istòria" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=1" title="Edita el codi de la secció: Istòria"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li eqüacions diferenciali son apareissudi a la fin dau sègle XVII emb l'invencion dau <a href="/wiki/Calcul_diferencial" class="mw-redirect" title="Calcul diferencial">calcul diferencial</a> per <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> (1642-1726) e per <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> (1646-1716). D'efècte, dins l'encastre dei sieus trabalhs, Newton identifiquèt tres eqüacions diferenciali e prepausèt d'exemples e de <a href="/wiki/Tecnica" title="Tecnica">tecnicas</a> de resolucion<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. Rapidament, aqueli eqüacions ocupèron una plaça importanta en <a href="/wiki/Fisica" title="Fisica">fisica</a>. Per exemple, tre lo 1695, Jakob Bernoulli identifiquèt l'<a href="/w/index.php?title=Eq%C3%BCacion_diferenciala_de_Bernoulli&action=edit&redlink=1" class="new" title="Eqüacion diferenciala de Bernoulli (la pagina existís pas)">eqüacion que pòrta lo sieu nom</a> dins l'encastre dei sieus trabalhs sus lo calcul diferencial<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>. Dins lo corrent dau sègle XVIII, l'importància d'aqueli eqüacions foguèt confirmada per la descubèrta d'autri relacions diferenciali dins mai d'un domeni<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>. Pauc a pauc, de <a href="/wiki/Matematicas" title="Matematicas">matematicians</a> comencèron d'estudis sistematics, cen que permetèt de descubrir e de resòlver d'eqüacions mai e mai complèxi. Uei, li eqüacions diferenciali pus simpli fan partida de l'<a href="/wiki/Educacion" title="Educacion">ensenhament</a> scientific segondari de mai d'un <a href="/wiki/Pa%C3%ADs" title="País">país</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Tipes_principals_d'eqüacions_diferenciali"><span id="Tipes_principals_d.27eq.C3.BCacions_diferenciali"></span>Tipes principals d'eqüacions diferenciali</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=2" title="Modificar la seccion : Tipes principals d'eqüacions diferenciali" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=2" title="Edita el codi de la secció: Tipes principals d'eqüacions diferenciali"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Li_eqüacions_diferenciali_ordinari"><span id="Li_eq.C3.BCacions_diferenciali_ordinari"></span>Li eqüacions diferenciali ordinari</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=3" title="Modificar la seccion : Li eqüacions diferenciali ordinari" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=3" title="Edita el codi de la secció: Li eqüacions diferenciali ordinari"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li <a href="/w/index.php?title=Eq%C3%BCacion_diferenciala_ordin%C3%A0ria&action=edit&redlink=1" class="new" title="Eqüacion diferenciala ordinària (la pagina existís pas)">eqüacions diferenciali ordinari</a> (EDO) son d'eqüacions diferenciali qu'establisson d'egalitats entre de <a href="/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas)">foncions</a> que dependon d'una variabla unica. Es lo tipe pus simple e de la sieua forma generala per una foncion <i>u</i> es : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u'(t)=K\,u(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>u</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>K</mi> <mspace width="thinmathspace" /> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u'(t)=K\,u(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0db08c63dd54e204f90e558797634a3fcab71a59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.193ex; height:3.009ex;" alt="{\displaystyle u'(t)=K\,u(t)}"></span></center> <p>Existisse una teoria ben desvolopada dei eqüacions diferenciali ordinari que permet de determinar l'existéncia de solucions, de prepausar un metòde de resolucion e d'estudiar li solucions possibli. Aqueu darrier aspècte a conoissut de desvolopaments consequents car es important en <a href="/wiki/Sci%C3%A9ncia" title="Sciéncia">sciéncia</a> per seleccionar li solucions aguent una realitat <a href="/wiki/Fisica" title="Fisica">fisica</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Li_eqüacions_diferenciali_parciali"><span id="Li_eq.C3.BCacions_diferenciali_parciali"></span>Li eqüacions diferenciali parciali</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=4" title="Modificar la seccion : Li eqüacions diferenciali parciali" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=4" title="Edita el codi de la secció: Li eqüacions diferenciali parciali"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li <a href="/w/index.php?title=Eq%C3%BCacion_diferenciala_parciala&action=edit&redlink=1" class="new" title="Eqüacion diferenciala parciala (la pagina existís pas)">eqüacions diferenciali parciali</a> (EDP) son d'eqüacions diferenciali qu'establisson d'egalitats entre de <a href="/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas)">foncions</a> que pòdon dependre de mai d'una variabla. Es un tipe pus complèxe que li eqüacions diferenciali ordinari. Per una foncion <i>y</i> dependenta dei variablas <i>x</i>, <i>y</i>, <i>z</i> e <i>t</i>, una eqüacion diferenciala parciala pòu pilhar la forma seguenta : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\partial ^{2}u \over \partial x^{2}}+{\partial ^{2}u \over \partial y^{2}}+{\partial ^{2}u \over \partial z^{2}}={1 \over c^{2}}{\partial ^{2}u \over \partial t^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\partial ^{2}u \over \partial x^{2}}+{\partial ^{2}u \over \partial y^{2}}+{\partial ^{2}u \over \partial z^{2}}={1 \over c^{2}}{\partial ^{2}u \over \partial t^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f1db5db1cb1a04af271fa86d3accf07c0604bcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:29.93ex; height:6.343ex;" alt="{\displaystyle {\partial ^{2}u \over \partial x^{2}}+{\partial ^{2}u \over \partial y^{2}}+{\partial ^{2}u \over \partial z^{2}}={1 \over c^{2}}{\partial ^{2}u \over \partial t^{2}}}"></span></center> <p>Aqueli eqüacions an sovent un nombre important de solucions car la multiplicitat dei variablas aumenta considerablament lo camp dei possibles. Li eqüacions diferenciali parciali son omnipresenti dins li <a href="/wiki/Sci%C3%A9ncia" title="Sciéncia">sciéncias</a>, especialament en <a href="/w/index.php?title=Dinamica_dei_estructuras&action=edit&redlink=1" class="new" title="Dinamica dei estructuras (la pagina existís pas)">dinamica dei estructuras</a>, en <a href="/w/index.php?title=Mecanica_dei_fluides&action=edit&redlink=1" class="new" title="Mecanica dei fluides (la pagina existís pas)">mecanica dei fluides</a>, dins li teorias de la <a href="/wiki/Gravitacion" title="Gravitacion">gravitacion</a>, dins li teorias de la <a href="/wiki/Mecanica_quantica" title="Mecanica quantica">mecanica quantica</a> e en <a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagnetisme</a>. Son finda centrali en simulacion <a href="/wiki/Aeronautica" title="Aeronautica">aeronautica</a>, en sintèsi d'imatges e en <a href="/wiki/Meteorologia" title="Meteorologia">meteorologia</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Li_eqüacions_diferenciali_non_lineari"><span id="Li_eq.C3.BCacions_diferenciali_non_lineari"></span>Li eqüacions diferenciali non lineari</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=5" title="Modificar la seccion : Li eqüacions diferenciali non lineari" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=5" title="Edita el codi de la secció: Li eqüacions diferenciali non lineari"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li eqüacions diferenciali non lineari son d'eqüacions diferenciali implicant de foncions non lineari. Un exemple d'aqueu tipe d'eqüacion es, dins lo cas d'una <a href="/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas)">foncion</a> <i>u</i>, la relacion seguenta entre lo carrat d'aquela foncion e la sieua <a href="/wiki/Derivada" title="Derivada">derivada</a> primiera : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {du}{dx}}=-u^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>u</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {du}{dx}}=-u^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6899a5ebd039f236b442d307af38e91c45609d80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.672ex; height:5.509ex;" alt="{\displaystyle {\frac {du}{dx}}=-u^{2}}"></span></center> <p>Aqueli eqüacions son presenti dins de domenis variats e lu metòdes de resolucion dependon generalament dau problema estudiat. Per rapòrt ai eqüacions diferenciali lineari, una particularitat d'aqueli eqüacions es l'impossibilitat de sobrepauar doi solucions per formar una solucion novèla. Aquò es una especificitat importanta car, per li eqüacions lineari, aquela proprietat de sobreposicion es centrala dins mai d'una resolucion d'eqüacions. Li <a href="/w/index.php?title=Eq%C3%BCacions_de_Navier%E2%80%93Stokes&action=edit&redlink=1" class="new" title="Eqüacions de Navier–Stokes (la pagina existís pas)">eqüacions de Navier–Stokes</a> en <a href="/wiki/Fisica" title="Fisica">fisica</a> e li <a href="/w/index.php?title=Eq%C3%BCacions_de_Lotka%E2%80%93Volterra&action=edit&redlink=1" class="new" title="Eqüacions de Lotka–Volterra (la pagina existís pas)">eqüacions de Lotka–Volterra</a> en <a href="/wiki/Biologia" title="Biologia">biologia</a> ne'n son d'exemples caracteristics d'eqüacions diferenciali non lineari. </p> <div class="mw-heading mw-heading2"><h2 id="Resolucion_dei_eqüacions_diferenciali"><span id="Resolucion_dei_eq.C3.BCacions_diferenciali"></span>Resolucion dei eqüacions diferenciali</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=6" title="Modificar la seccion : Resolucion dei eqüacions diferenciali" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=6" title="Edita el codi de la secció: Resolucion dei eqüacions diferenciali"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Existéncia_de_solucions"><span id="Exist.C3.A9ncia_de_solucions"></span>Existéncia de solucions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=7" title="Modificar la seccion : Existéncia de solucions" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=7" title="Edita el codi de la secció: Existéncia de solucions"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'existéncia de solucions a una eqüacion diferenciala non es evidenta. De <a href="/wiki/Teor%C3%A8ma" title="Teorèma">teoremas</a> existisson per determinar aquela existéncia coma lo <a href="/w/index.php?title=Teorema_de_Cauchy-Peano-Arzel%C3%A0&action=edit&redlink=1" class="new" title="Teorema de Cauchy-Peano-Arzelà (la pagina existís pas)">teorema de Cauchy-Peano-Arzelà</a>. Dins fòrça cas, en particular aquelu que regardan de problemas reaus, cau finda tenir còmpte dei valors conoissudi dau problema. D'efècte, quand un nombre fòrça important de solucions existisson, es necessari d'utilizar aquela valor per seleccionar la solucion que respècta li constrenchas fixadi per la realitat. </p> <div class="mw-heading mw-heading3"><h3 id="Quaucu_cas_simples">Quaucu cas simples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=8" title="Modificar la seccion : Quaucu cas simples" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=8" title="Edita el codi de la secció: Quaucu cas simples"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Eqüacions_diferenciali_ordinari_dau_promier_gra"><span id="Eq.C3.BCacions_diferenciali_ordinari_dau_promier_gra"></span>Eqüacions diferenciali ordinari dau promier gra</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=9" title="Modificar la seccion : Eqüacions diferenciali ordinari dau promier gra" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=9" title="Edita el codi de la secció: Eqüacions diferenciali ordinari dau promier gra"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li eqüacions diferenciali ordinari dau promier gra son de la forma : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ay'+by=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>b</mi> <mi>y</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ay'+by=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e645b259dd199a965fe39603f277d505b4a8d89b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.174ex; height:2.843ex;" alt="{\displaystyle ay'+by=c}"></span></center> <p>S'estúdia primierament l'eqüacion lineara omogenea associada, es a dire <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ay'+by=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>b</mi> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ay'+by=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4c3cb59196ef16e631e2b848f002a5fc1ab5d39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.329ex; height:2.843ex;" alt="{\displaystyle ay'+by=0}"></span>. Li sieui solucions son <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=K\mathrm {e} ^{-A(x)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>K</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y(x)=K\mathrm {e} ^{-A(x)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe0c80f401ffc272fe17e0373834772c36787c31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.454ex; height:3.343ex;" alt="{\displaystyle y(x)=K\mathrm {e} ^{-A(x)}}"></span>, emb <i>A</i> una primitiva de <i>a</i> e <i>K</i> una constanta reala que que sigue. Per resòlver l'eqüacion iniciala, es necessari d'ajustar una solucion particulara d'aquela eqüacion a la solucion generala de l'eqüacion omogenea. </p> <div class="mw-heading mw-heading4"><h4 id="Eqüacions_diferenciali_ordinari_dau_segond_gra"><span id="Eq.C3.BCacions_diferenciali_ordinari_dau_segond_gra"></span>Eqüacions diferenciali ordinari dau segond gra</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=10" title="Modificar la seccion : Eqüacions diferenciali ordinari dau segond gra" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=10" title="Edita el codi de la secció: Eqüacions diferenciali ordinari dau segond gra"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li eqüacions diferenciali ordinari dau segond gra son de la forma : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ay''+by'+cy=d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>y</mi> <mo>″</mo> </msup> <mo>+</mo> <mi>b</mi> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>c</mi> <mi>y</mi> <mo>=</mo> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ay''+by'+cy=d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67c93de4ca32888ba505144680eb225b90eb4697" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.528ex; height:2.843ex;" alt="{\displaystyle ay''+by'+cy=d}"></span></center> <p>Per resòlver una tala eqüacion, cau primierament l'<a href="/w/index.php?title=Eq%C3%BCacion_caracteristica&action=edit&redlink=1" class="new" title="Eqüacion caracteristica (la pagina existís pas)">eqüacion caracteristica</a> de l'eqüacion diferenciala qu'es egala a : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\lambda ^{2}+b\lambda +c=0.~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>λ</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>0.</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\lambda ^{2}+b\lambda +c=0.~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e12e4333cdf78ef6fe8ae21d5cef7861114f98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:18.168ex; height:2.843ex;" alt="{\displaystyle a\lambda ^{2}+b\lambda +c=0.~}"></span>Dins lo cas de coefficients reaus, lo determinant <i>Δ</i> d'aquela eqüacion permet de descriure l'existéncia e la forma dei solucions eventuali : </p> <ul><li>si <i>Δ</i> > 0, l'eqüacion caracteristica a doi solucions reali <i>λ</i><sub><small>1</small></sub> e <i>λ</i><sub><small>2</small></sub>. Li solucions de l'eqüacion diferenciala son alora de la forma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=A{\rm {e}}^{\lambda _{1}x}+B{\rm {e}}^{\lambda _{2}x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>x</mi> </mrow> </msup> <mo>+</mo> <mi>B</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>x</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=A{\rm {e}}^{\lambda _{1}x}+B{\rm {e}}^{\lambda _{2}x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6b9e3042b63a7836541a8ce053e792d0edc8e1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.853ex; height:3.176ex;" alt="{\displaystyle f(x)=A{\rm {e}}^{\lambda _{1}x}+B{\rm {e}}^{\lambda _{2}x}}"></span> emb <i>A</i> e <i>B</i> doi reaus de determinar segon li condicions iniciali associadi a l'eqüacion.</li> <li>si <i>Δ</i> = 0, l'eqüacion caracteristica a una solucion unica <i>λ</i>. Li solucions de l'eqüacion diferenciala son alora de la forma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=(Ax+B){\rm {e}}^{\lambda x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mi>x</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mi>x</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=(Ax+B){\rm {e}}^{\lambda x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95198bd3f53f590e9582a5c0291c108fb6a6b4c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.166ex; height:3.176ex;" alt="{\displaystyle f(x)=(Ax+B){\rm {e}}^{\lambda x}}"></span> emb <i>A</i> e <i>B</i> doi reaus de determinar segon li condicions iniciali associadi a l'eqüacion.</li> <li>si <i>Δ</i> < 0, l'eqüacion caracteristica a doi solucions complèxi <i>u</i> + <i>iv</i> et <i>u</i> - <i>iv</i>. Li solucions de l'eqüacion diferenciala son alora de la forma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\rm {e}}^{ux}(A\cos(|v|x)+B\sin(|v|x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> <mi>x</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>A</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>B</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\rm {e}}^{ux}(A\cos(|v|x)+B\sin(|v|x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13eee4b92bf3dd1061bdc33f51b336823736b775" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.679ex; height:2.843ex;" alt="{\displaystyle f(x)={\rm {e}}^{ux}(A\cos(|v|x)+B\sin(|v|x))}"></span> emb <i>A</i> e <i>B</i> doi reaus de determinar segon li condicions iniciali associadi a l'eqüacion.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Aplicacions">Aplicacions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=11" title="Modificar la seccion : Aplicacions" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=11" title="Edita el codi de la secció: Aplicacions"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li eqüacions diferenciali an d'aplicacions importanti en <a href="/wiki/Sci%C3%A9ncia" title="Sciéncia">sciéncias</a> e en <a href="/wiki/Engenhari%C3%A1" title="Engenhariá">engenharia</a>. Son ensinda l'objècte d'estudis encara importants per li matematicas teoriqui per cercar l'existéncia de solucions e estudiar lu metòdes generals de resolucion. En parallèle, li <a href="/wiki/Matematicas" title="Matematicas">matematicas</a> aplicadi s'interèssan a la determinacion de solucions particulari a de problemas concrets. Mai d'una lei fondamentala en <a href="/wiki/Fisica" title="Fisica">fisica</a> e en <a href="/wiki/Quimia" title="Quimia">quimia</a> son escrichi sota la forma d'eqüacion diferenciala e, d'una maniera generala, lo <a href="/wiki/Calcul_infinitesimal" title="Calcul infinitesimal">calcul diferencial</a> es fòrça present dins aqueli disciplinas. En <a href="/wiki/Biologia" title="Biologia">biologia</a> e en engenharia, la modelizacion de fenomènes reaus implica egalament l'utilizacion regulara d'eqüacions diferenciali. </p> <div class="mw-heading mw-heading2"><h2 id="Annèxas"><span id="Ann.C3.A8xas"></span>Annèxas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=12" title="Modificar la seccion : Annèxas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=12" title="Edita el codi de la secció: Annèxas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ligams_intèrnes"><span id="Ligams_int.C3.A8rnes"></span>Ligams intèrnes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=13" title="Modificar la seccion : Ligams intèrnes" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=13" title="Edita el codi de la secció: Ligams intèrnes"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="-moz-column-count:4; column-count:4;"> <ul><li><a href="/wiki/Alg%C3%A8bra" title="Algèbra">Algèbra</a>.</li> <li><a href="/wiki/Calcul_diferencial" class="mw-redirect" title="Calcul diferencial">Calcul diferencial</a>.</li> <li><a href="/w/index.php?title=Condicion_iniciala&action=edit&redlink=1" class="new" title="Condicion iniciala (la pagina existís pas)">Condicion iniciala</a>.</li> <li><a href="/wiki/Derivada" title="Derivada">Derivada</a>.</li> <li><a href="/w/index.php?title=Derivada_parciala&action=edit&redlink=1" class="new" title="Derivada parciala (la pagina existís pas)">Derivada parciala</a>.</li> <li><a href="/wiki/Eq%C3%BCacion" class="mw-redirect" title="Eqüacion">Eqüacion</a>.</li> <li><a href="/w/index.php?title=Eq%C3%BCacion_caracteristica&action=edit&redlink=1" class="new" title="Eqüacion caracteristica (la pagina existís pas)">Eqüacion caracteristica</a>.</li> <li><a href="/w/index.php?title=Eq%C3%BCacion_diferenciala_ordin%C3%A0ria&action=edit&redlink=1" class="new" title="Eqüacion diferenciala ordinària (la pagina existís pas)">Eqüacion diferenciala ordinària</a>.</li> <li><a href="/w/index.php?title=Eq%C3%BCacion_diferenciala_parciala&action=edit&redlink=1" class="new" title="Eqüacion diferenciala parciala (la pagina existís pas)">Eqüacion diferenciala parciala</a>.</li> <li><a href="/w/index.php?title=Eq%C3%BCacion_integrala&action=edit&redlink=1" class="new" title="Eqüacion integrala (la pagina existís pas)">Eqüacion integrala</a>.</li> <li><a href="/w/index.php?title=Eq%C3%BCacion_integrodiferenciala&action=edit&redlink=1" class="new" title="Eqüacion integrodiferenciala (la pagina existís pas)">Eqüacion integrodiferenciala</a>.</li> <li><a href="/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas)">Foncion</a>.</li> <li><a href="/w/index.php?title=Integrala&action=edit&redlink=1" class="new" title="Integrala (la pagina existís pas)">Integrala</a>.</li> <li><a href="/wiki/Matematicas" title="Matematicas">Matematicas</a>.</li> <li><a href="/w/index.php?title=Relacion_de_recurr%C3%A9ncia&action=edit&redlink=1" class="new" title="Relacion de recurréncia (la pagina existís pas)">Relacion de recurréncia</a>.</li> <li><a href="/w/index.php?title=Sistema_d%27eq%C3%BCacions_diferenciali&action=edit&redlink=1" class="new" title="Sistema d'eqüacions diferenciali (la pagina existís pas)">Sistema d'eqüacions diferenciali</a>.</li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Bibliografia">Bibliografia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=14" title="Modificar la seccion : Bibliografia" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=14" title="Edita el codi de la secció: Bibliografia"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>W. E. Boyce e R. C. DiPrima, <i>Elementary Differential Equations and Boundary Value Problems</i>, Nòva York, Wiley, 4<sup>a</sup> edicion, 1986.</li> <li>Jean-Pierre Demailly, <i>Analyse numérique et équations différentielles</i>, Grenòble, Presses universitaires de Grenoble, 1996.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Nòtas_e_referéncias"><span id="N.C3.B2tas_e_refer.C3.A9ncias"></span>Nòtas e referéncias</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equacion_diferenciala&veaction=edit&section=15" title="Modificar la seccion : Nòtas e referéncias" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Equacion_diferenciala&action=edit&section=15" title="Edita el codi de la secció: Nòtas e referéncias"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Lo Congrès Permanent de la Lenga Occitana, <i>Dicod'Òc</i>, recèrca « équation », consultat lo 28 de novembre dau 2023, <a rel="nofollow" class="external autonumber" href="https://dicodoc.eu/fr/dictionnaires?option=com_dicodoc&view=search&Itemid=683&type=fr-oc&dic%5B%5D=BASIC&dic%5B%5D=RBVD&dic%5B%5D=ALPC&dic%5B%5D=ATAU&dic%5B%5D=PROV&dic%5B%5D=PNST&dic%5B%5D=OMLH&dic%5B%5D=LAUS&dic%5B%5D=LAGA&dic%5B%5D=LEMO&q=%C3%A9quation&q2=&submit=Rechercher">[1]</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Isaac Newton, <i>Methodus Fluxionum et Serierum Infinitarum</i>, Opuscula, 1744, Vol. I. p. 66.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Ernst Hairer, Syvert Paul Nørsett e Gerhard Wanner, <i>Solving ordinary differential equations I: Nonstiff problems</i>, Springer-Verlag, 1993.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">David Speiser, <i>Discovering the Principles of Mechanics 1600-1800</i>, Birkhäuser, 2008, p. 191.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Craig Frasier, « Review of The evolution of dynamics, vibration theory from 1687 to 1742, by John T. Cannon and Sigalia Dostrovsky », <i>Bulletin of the American Mathematical Society. New Series</i>, vol. 9, n° 1, julhet dau 1983.</span> </li> </ol>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Recuperada de « <a dir="ltr" href="https://oc.wikipedia.org/w/index.php?title=Equacion_diferenciala&oldid=2409336">https://oc.wikipedia.org/w/index.php?title=Equacion_diferenciala&oldid=2409336</a> »</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categorias de la pagina</a> : <ul><li><a href="/w/index.php?title=Categoria:P%C3%A0gines_amb_mides_d%27imatge_que_contenen_px_addicionals&action=edit&redlink=1" class="new" title="Categoria:Pàgines amb mides d'imatge que contenen px addicionals (la pagina existís pas)">Pàgines amb mides d'imatge que contenen px addicionals</a></li><li><a href="/wiki/Categoria:Article_redigit_en_ni%C3%A7ard" title="Categoria:Article redigit en niçard">Article redigit en niçard</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Aquela pagina es estada modificada pel darrièr còp lo 28 novembre de 2023 a 13.58.</li> <li id="footer-info-copyright"><span style="white-space: normal"><a href="/wiki/Wikip%C3%A8dia:Drech_d%27autor" title="Wikipèdia:Drech d'autor">Drech d'autor</a> : Los tèxtes son disponibles jos <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.fr">licéncia Creative Commons paternitat pertatge a l’identic</a> ; d’autras condicions se pòdon aplicar. 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