{"id":233968,"date":"2022-06-28T17:19:00","date_gmt":"2022-06-28T15:19:00","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=233968"},"modified":"2024-08-28T22:45:24","modified_gmt":"2024-08-28T20:45:24","slug":"equation-differentielle-du-premier-ordre","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/equation-differentielle-du-premier-ordre\/","title":{"rendered":"Comment r\u00e9soudre une \u00e9quation diff\u00e9rentielle du premier ordre ?"},"content":{"rendered":"\n<p>Vous cherchez \u00e0 r\u00e9soudre une <strong>\u00e9quation diff\u00e9rentielle du premier ordre<\/strong> ? Rassurez-vous, vous \u00eates au bon endroit ! Gr\u00e2ce \u00e0 ce cours d\u00e9di\u00e9 \u00e0 la r\u00e9solution d’<strong>\u00e9quation diff\u00e9rentielle du premier ordre<\/strong>, vous profitez de conseils m\u00e9thodologiques de pointe pour faire face \u00e0 ce type d’exercices.<\/p>\n<p>Et si tu te sens toujours perdu avec ces \u00e9quations, nos <a href=\"https:\/\/sherpas.com\/cours\/maths\"><strong>cours de soutien en math\u00e9matiques<\/strong><\/a>\u00a0sont l\u00e0 pour \u00eatre ta bou\u00e9e de sauvetage dans cette mer complexe de fonctions ! \ud83c\udf0a<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">M\u00e9thode 1 : R\u00e9soudre une \u00e9quation diff\u00e9rentielle du premier degr\u00e9.<\/h2>\n\n\n\n<p><\/p>\nR\u00e9soudre l’\u00e9quation diff\u00e9rentielle sur <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5bad56d5bf33fcca72a925418faff9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\mathbb{R}_+^*\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -6px;\"\/> :\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 22px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-b9430c543c66116387f27664c31ba198_l3.png\" height=\"22\" width=\"258\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\[(E)\;\;t(1+\ln(t)^2)y'+2\ln(t)y=1.\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Conseils m\u00e9thodologiques<\/h4>\n\n\n\n<p><\/p>\nOn souhaite r\u00e9soudre l’\u00e9quation <p class=\"ql-center-displayed-equation\" style=\"line-height: 21px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-ab5466da4259899f2bdde31041555871_l3.png\" height=\"21\" width=\"264\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\[(E)\;\;\;\;\forall t\in I,\; a(t)y'+b(t)y=c(t),\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\navec <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, 3 fonctions continues sur un intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-a6e421454947c585b8fb5ae10299f873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> et \u00e0 valeurs dans <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3080e0ba24b7356a2a94263a10b2c380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\mathbb{K}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>.\n\n\n<li> On normalise l’\u00e9quation diff\u00e9rentielle, quitte \u00e0 d\u00e9couper l’intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>. On est amen\u00e9 \u00e0 r\u00e9soudre <p class=\"ql-center-displayed-equation\" style=\"line-height: 21px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-16d4c8d53315b384a2f68d00903753a7_l3.png\" height=\"21\" width=\"258\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\[(E_1)\;\;\;\;\forall t\in I,\; y'+a_1(t)y=b_1(t).\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p> <\/li>\n\n<li> On d\u00e9termine une primitive de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-460f5abc45b558edf34fe288dc0a9979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/> pour trouver l’ensemble des solutions \u00e0 l’\u00e9quation homog\u00e8ne associ\u00e9e \u00e0 <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-27e7dba402a9314ea13e2bdae585e11d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(E_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/>. <\/li>\n<li> On cherche une solution particuli\u00e8re de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-27e7dba402a9314ea13e2bdae585e11d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(E_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/>, pour cela plusieurs solutions : <\/li>\n – une solution simple et \u00e9vidente fonctionne; <br>\n – le second membre est de la forme <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-972680ff4fdd9b3d3e4270f6ddc0f92f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(t)e^{\lambda t}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"55\" style=\"vertical-align: -5px;\"\/> o\u00f9 <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> est une fonction polynomiale; <br>\n – on utilise la m\u00e9thode de la variation de la constante. <br>\nSi le second membre est sous la forme d’une somme de fonction, on pourra utiliser le principe de superposition.\n<li> On trouve l’ensemble des solutions de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-409116cebc012d88ab8959f53d9e8257_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(E)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"\/>. <\/li>\n\n\n\n<h3 class=\"wp-block-heading\">Application de la m\u00e9thode<\/h3>\n\n\n\n<p><\/p>\n<li> On normalise l’\u00e9quation diff\u00e9rentielle : <p class=\"ql-center-displayed-equation\" style=\"line-height: 43px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3d1c956458ded82d4755a236bdcf80bf_l3.png\" height=\"43\" width=\"380\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\[(E_1)\;\;\;\;\forall t\in I,\; y'+\dfrac{2\ln(t)}{t(1+\ln(t)^2)}y=\dfrac{1}{t(1+\ln(t)^2)}.\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p> <\/li>\n<li> On d\u00e9termine une primitive de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9d80381e1a753826416e720d31553052_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\mapsto \dfrac{2\ln(t)}{t(1+\ln(t)^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"130\" style=\"vertical-align: -17px;\"\/>.<\/li> <br>\nCette fonction est sous la forme <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-946efd1878037dc942f1ae597613f1ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\dfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"15\" style=\"vertical-align: -12px;\"\/> avec <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-b26cd7951f7ffcfa64b33026e564faa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"u:t\mapsto 1+\ln(t)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"131\" style=\"vertical-align: -5px;\"\/>. Une primitive de cette fonction est <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f7cf159bdda55df3433d0b02ba1ede53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\displaystyle t\mapsto \ln\left(1+\ln(t)^2\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"139\" style=\"vertical-align: -7px;\"\/>.\n<li> Les solutions de l’\u00e9quation homog\u00e8ne sont les fonctions <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-76b54e816ea646376e153319d5da2e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\longmapsto Ce^{-\ln\left(1+\ln(t)^2\right)}=\dfrac{C}{1+\ln(t)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"257\" style=\"vertical-align: -17px;\"\/> avec <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-bde37c3960111e24f6ba150ff99c353d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C\in \mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: -1px;\"\/>. <\/li>\n<li> On cherche une solution particuli\u00e8re de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-27e7dba402a9314ea13e2bdae585e11d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(E_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/>, on va utiliser la m\u00e9thode de la variation de la constante. <\/li> <br>\nOn cherche une solution particuli\u00e8re de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-27e7dba402a9314ea13e2bdae585e11d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(E_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> sous la forme <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-cd92e5e1a7df60bc33f2a8027974f052_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_1: t\longmapsto \dfrac{C(t)}{1+\ln(t)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"152\" style=\"vertical-align: -17px;\"\/> o\u00f9 <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> est une fonction d\u00e9rivable sur <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5bad56d5bf33fcca72a925418faff9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\mathbb{R}_+^*\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -6px;\"\/>. On a alors :\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18a1ed23384ab5f3086e38b5fb53c712_l3.png\" height=\"36\" width=\"139\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\[\forall t\in I,\; C'(t)=\dfrac{1}{t}.\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\nOn en d\u00e9duit que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f5cc5dd8c68c6bc3d165b2b7acdb48b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C:t\longmapsto \ln(t)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"\/>. On obtient la solution particuli\u00e8re suivante : <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-7ca51214982520836d9578fcf0f2f2b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\mapsto \dfrac{\ln(t)}{1+\ln(t)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"110\" style=\"vertical-align: -17px;\"\/>.\n<li> L’ensemble des solutions de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-409116cebc012d88ab8959f53d9e8257_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(E)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"\/> est :\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 43px;\"><span class=\"ql-right-eqno\"> <\/span><span class=\"ql-left-eqno\"> <\/span><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-cced61cb473e084e4976ac8c01256367_l3.png\" height=\"43\" width=\"241\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\[\mathcal{S}=\left\{t\mapsto \dfrac{C+\ln(t)}{1+\ln(t)^2},\; C\in\mathbb{R}\right\} .\]\" title=\"Rendered by QuickLaTeX.com\"\/><\/p> <\/li>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-1 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:30%\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.vuibert.fr\/ouvrage\/9782311408720-mathematiques-mpsi-mp2i-tout-en-un\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/03\/livre-maths-mpsi-vuibert-751x1024.jpg\" alt=\"livre maths mpsi vuibert\" class=\"wp-image-216756\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:10%\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:60%\">\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Cet article est extrait de l’ouvrage <em><a href=\"https:\/\/www.vuibert.fr\/ouvrage\/9782311408720-mathematiques-mpsi-mp2i-tout-en-un\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">Maths MPSI-MP2I. Tout-en-un : cours, m\u00e9thodes, entra\u00eenement et corrig\u00e9s <\/a><\/em>(\u00e9ditions Vuibert, juin 2021)<em> <\/em>\u00e9crit par <em>E. Thomas, S. Bellec, G. Boutard. ISBN n\u00b09782311408720<\/em><\/p>\n<\/div>\n<\/div>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n data-payload='{"align":"center","id":"233968","slug":"default","valign":"bottom","ignore":"","reference":"auto","class":"","count":"0","legendonly":"","readonly":"","score":"0","starsonly":"","best":"5","gap":"5","greet":"Tu as aim\u00e9 cet article ?","legend":"0\\\/5 - (0 vote)","size":"24","title":"Comment r\u00e9soudre une \u00e9quation diff\u00e9rentielle du premier ordre ?","width":"0","_legend":"{score}\\\/{best} - ({count} {votes})","font_factor":"1.25"}'>\n \n<div class=\"kksr-stars\">\n \n<div class=\"kksr-stars-inactive\">\n <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <\/div>\n \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n <div class=\"kksr-star\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <div class=\"kksr-star\" style=\"padding-right: 5px\">\n \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n <\/div>\n <\/div>\n<\/div>\n \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n <span class=\"kksr-muted\">Tu as aim\u00e9 cet article ?<\/span>\n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Vous cherchez \u00e0 r\u00e9soudre une \u00e9quation diff\u00e9rentielle du premier ordre ? Rassurez-vous, vous \u00eates au bon endroit ! (…)<\/p>\n","protected":false},"author":158,"featured_media":194520,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[803,810],"tag":[78,345],"class_list":["post-233968","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-prepa","tag-prepa-scientifique"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/233968","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/158"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=233968"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/233968\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/194520"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=233968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=233968"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=233968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}