{"id":23355,"date":"2022-05-28T21:27:42","date_gmt":"2022-05-28T21:27:42","guid":{"rendered":"https:\/\/onlinemathtutor.co\/?page_id=23355"},"modified":"2023-04-21T00:49:56","modified_gmt":"2023-04-21T00:49:56","slug":"virtual-lessons-de-exact","status":"publish","type":"page","link":"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/virtual-lessons-de-exact\/","title":{"rendered":"Virtual Lessons &#8211; DE &#8211; [Separable]"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"23355\" class=\"elementor elementor-23355\" data-elementor-post-type=\"page\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-612ca942 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"612ca942\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2c461c5e\" data-id=\"2c461c5e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7810cb25 elementor-widget elementor-widget-heading\" data-id=\"7810cb25\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Virtual Lessons: Exact DEs<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-53362f6e elementor-section-stretched elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"53362f6e\" data-element_type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1534f332\" data-id=\"1534f332\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4ed7f52b elementor-nav-menu__align-center elementor-nav-menu--stretch elementor-nav-menu__text-align-center animated-fast elementor-nav-menu--dropdown-tablet elementor-nav-menu--toggle elementor-nav-menu--burger elementor-widget elementor-widget-nav-menu\" data-id=\"4ed7f52b\" data-element_type=\"widget\" data-settings=\"{&quot;submenu_icon&quot;:{&quot;value&quot;:&quot;&lt;i class=\\&quot;fas fa-pencil-alt\\&quot;&gt;&lt;\\\/i&gt;&quot;,&quot;library&quot;:&quot;fa-solid&quot;},&quot;full_width&quot;:&quot;stretch&quot;,&quot;_animation&quot;:&quot;none&quot;,&quot;layout&quot;:&quot;horizontal&quot;,&quot;toggle&quot;:&quot;burger&quot;}\" data-widget_type=\"nav-menu.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<nav aria-label=\"Menu\" class=\"elementor-nav-menu--main elementor-nav-menu__container elementor-nav-menu--layout-horizontal e--pointer-double-line e--animation-fast\">\n\t\t\t\t<ul id=\"menu-1-4ed7f52b\" class=\"elementor-nav-menu\"><li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23492\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-separable\/\" class=\"elementor-item\">Separable DEs<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23427\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-intfactor\/\" class=\"elementor-item\">Integrating Factor<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23430\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-exact\/\" class=\"elementor-item\">Exact DEs<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23428\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-firstordersub\/\" class=\"elementor-item\">Substitution<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t<div class=\"elementor-menu-toggle\" role=\"button\" tabindex=\"0\" aria-label=\"Menu Toggle\" aria-expanded=\"false\">\n\t\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--open eicon-menu-bar\"><\/i><i aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--close eicon-close\"><\/i>\t\t<\/div>\n\t\t\t\t\t<nav class=\"elementor-nav-menu--dropdown elementor-nav-menu__container\" aria-hidden=\"true\">\n\t\t\t\t<ul id=\"menu-2-4ed7f52b\" class=\"elementor-nav-menu\"><li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23492\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-separable\/\" class=\"elementor-item\" tabindex=\"-1\">Separable DEs<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23427\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-intfactor\/\" class=\"elementor-item\" tabindex=\"-1\">Integrating Factor<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23430\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-exact\/\" class=\"elementor-item\" tabindex=\"-1\">Exact DEs<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-23428\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/practice-problems-de-firstordersub\/\" class=\"elementor-item\" tabindex=\"-1\">Substitution<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-33c9ab82 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"33c9ab82\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-82444a8 elementor-widget elementor-widget-accordion\" data-id=\"82444a8\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1361\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1361\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><i class=\"fas fa-book-reader\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><i class=\"fas fa-book-reader\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Exact Differential Equations<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1361\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1361\"><p style=\"text-align: justify;\"><span style=\"font-size: 18px;\"><strong>Exact differential equations<\/strong> are a special type of differential equation that can be solved using a unique technique known as the method of integrating factors. An exact differential equation can be identified by checking whether the partial derivatives of the equation with respect to its variables are equal. In this tutorial, we will explore the steps involved in solving exact differential equations, including identifying an equation as exact, finding the integrating factor, and solving for the general solution\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">\nThe general formula for an exact differential equation is \\(M(x,y)dx + N(x,y)dy = 0 \\) where \\(M(x,y)\\) and \\(N(x,y)\\) are functions of \\(x\\)and \\(y\\). To solve an exact differential equation, we need to determine whether there exists a function \\(\\psi(x,y)\\) such that \\(\\frac{\\partial \\psi}{\\partial x} = M(x,y), \\quad \\frac{\\partial \\psi}{\\partial y} = N(x,y)\\)\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">\nIf such a function exists, then the differential equation is exact, and we can solve it by finding \\(\\psi(x,y)\\) and setting it equal to a constant \\(C\\). However, if such a function does not exist, we need to find an integrating factor \\(\\mu(x,y)\\) that will transform the differential equation into an exact one. The integrating factor is given by:\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">\n\\(\\mu(x,y) = e^{\\int P(x)dx}\\)\nwhere \\(P(x)\\) is the coefficient of \\(dx\\) in the expression for \\(M(x,y)dx + N(x,y)dy = 0\\). By multiplying both sides of the differential equation by \\(\\mu(x,y)\\) and applying the method of integrating factors, we can find \\(\\psi(x,y)\\) and solve for the general solution of the differential equation.\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Solving exact differential equations. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\"> <strong><a href=\"https:\/\/onlinemathtutor.co\/index.php\/course-content\/integration\/integration-formulas-update\/\" target=\"_blank\" rel=\"noopener\">See Integral Formulas<\/a><\/strong>.\u00a0<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-78857f74 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"78857f74\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ba1ece3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ba1ece3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-303ce68\" data-id=\"303ce68\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3fef961 elementor-widget elementor-widget-presto_video\" data-id=\"3fef961\" data-element_type=\"widget\" data-widget_type=\"presto_video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<!--presto-player:video_id=5--><figure class=\"wp-block-video presto-block-video  presto-provider-self-hosted\" style=\"--plyr-color-main: var(--presto-player-highlight-color, #294a70); --presto-player-logo-width: 150px; \">\n    <presto-player  id=\"presto-player-1\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/Virtual-Lessons\/DE\/Unit01\/Exact\/Lesson1.4-Exact[EX01].mp4\" media-title=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/Virtual-Lessons\/DE\/Unit01\/Exact\/Lesson1.4-Exact%5BEX01%5D.mp4\" css=\"\" class=\"presto-video-id-5 presto-preset-id-2 skin-modern\" skin=\"modern\" icon-url=\"https:\/\/onlinemathtutor.co\/wp-content\/plugins\/presto-player\/img\/sprite.svg\" preload=\"\" poster=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2023\/04\/OMT-VideoPoster.png\" playsinline  >\n                    <video controls preload=\"none\">\n            <source src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/Virtual-Lessons\/DE\/Unit01\/Exact\/Lesson1.4-Exact[EX01].mp4\" \/>\n        <\/video>\n    \n\n    <\/presto-player>\n<\/figure>\t\t<script>\n\t\t\tvar player = document.querySelector('presto-player#presto-player-1');\n\t\t\tplayer.video_id = 5;\n\t\t\t\t\t\t\t\t\t\t\t\tplayer.preset = {\"id\":2,\"name\":\"Course\",\"slug\":\"course\",\"icon\":\"welcome-learn-more\",\"skin\":\"modern\",\"play-large\":true,\"rewind\":true,\"play\":true,\"fast-forward\":true,\"progress\":true,\"current-time\":true,\"mute\":true,\"volume\":true,\"speed\":true,\"pip\":true,\"fullscreen\":true,\"captions\":false,\"reset_on_end\":true,\"auto_hide\":true,\"captions_enabled\":false,\"save_player_position\":true,\"sticky_scroll\":true,\"sticky_scroll_position\":\"bottom 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elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5f9be761\" data-id=\"5f9be761\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-419d0217 elementor-widget elementor-widget-spacer\" data-id=\"419d0217\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cfdc555 elementor-align-left elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"cfdc555\" data-element_type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/onlinemathtutor.co\/index.php\/course-content\/differential-equations-resources\/first-order-de\/problem-set-de-firstorder\/\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-arrow-circle-right\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Back To Main Page: First-Order Differential Equations<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5fd7ff9a elementor-widget elementor-widget-spacer\" data-id=\"5fd7ff9a\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div 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decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-22284\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/numerical-solutions-of-odes\/\" class=\"elementor-item\" tabindex=\"-1\">Numerical<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-24025\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/numerical-solutions-of-odes\/problem-set-de-numerical\/\" class=\"elementor-sub-item\" tabindex=\"-1\"><img decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-596f85de\" data-id=\"596f85de\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-12766046 elementor-widget elementor-widget-spacer\" data-id=\"12766046\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Virtual Lessons: Exact DEs Exact Differential Equations Exact differential equations are a special type of differential equation that can be solved using a unique technique known as the method of integrating factors. An exact differential equation can be identified by <a href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/virtual-lessons-de-exact\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":22250,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-23355","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Virtual Lessons - DE - [Separable] | Online Math Tutoring LLC | Expert Math Tutor Near Me<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/onlinemathtutor.co\/course-content\/differential-equations-resources\/first-order-de\/virtual-lessons-de-exact\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Virtual Lessons - DE - [Separable] | Online Math Tutoring LLC | Expert Math Tutor Near Me\" \/>\n<meta property=\"og:description\" content=\"Virtual Lessons: Exact DEs Exact Differential Equations Exact differential equations are a special type of differential equation that can be solved using a unique technique known as the method of integrating factors. 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