{"id":154504,"date":"2022-03-25T23:36:31","date_gmt":"2022-03-25T18:06:31","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/first-order-differential-equation-2\/"},"modified":"2022-12-31T16:06:18","modified_gmt":"2022-12-31T10:36:18","slug":"first-order-differential-equation-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/first-order-differential-equation\/","title":{"rendered":"First Order Differential Equation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/first-order-differential-equation\/#Explain_in_Detail_General_Solution_of_1st_Order_Differential_Equation\" title=\"Explain in Detail :General Solution of 1st Order Differential Equation\">Explain in Detail :General Solution of 1st Order Differential Equation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/first-order-differential-equation\/#First-Order_Differential_Equation\" title=\"First-Order Differential Equation\">First-Order Differential Equation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/first-order-differential-equation\/#First_Order_Linear_Differential_Equation\" title=\"First Order Linear Differential Equation\">First Order Linear Differential Equation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/first-order-differential-equation\/#How_to_Solve_1st_Order_Differential_Equations\" title=\"How to Solve 1st Order Differential Equations?\">How to Solve 1st Order Differential Equations?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/first-order-differential-equation\/#Solving_1st_order_differential_equations_can_be_tedious_but_the_two_approaches_mentioned_below_can_ease_things_out\" title=\"Solving 1st order differential equations can be tedious but the two approaches mentioned below can ease things out.\">Solving 1st order differential equations can be tedious but the two approaches mentioned below can ease things out.<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Explain_in_Detail_General_Solution_of_1st_Order_Differential_Equation\"><\/span>Explain in Detail :General Solution of 1st Order Differential Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A first-order differential equation is an equation that describes the change in a function over time in terms of its first derivative. The general solution of a first-order differential equation is a function that solves the equation and includes all the arbitrary constants of integration.<\/p>\n<p>There are a few methods that can be used to find the general solution of a first-order differential equation. One method is to use the separation of variables technique. This technique involves dividing the equation into two parts: one that contains only the derivative and one that contains only the function. This technique can then be used to solve each of the two parts separately.<\/p>\n<p>Another method that can be used to find the general solution of a first-order differential equation is the integration technique. This technique involves integrating the equation to find the function. Once the function is found, the arbitrary constants of integration can be determined.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154503 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/first-order-differential-equation.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/first-order-differential-equation.jpg?v=1648231587 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/first-order-differential-equation-300x212.jpg?v=1648231587 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"First-Order_Differential_Equation\"><\/span>First-Order Differential Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A differential equation is an equation that relates a function and one or more of its derivatives. A first-order differential equation is a differential equation that has one derivative.<\/p>\n<p>The most common type of first-order differential equation is the linear equation. A linear equation is an equation in which the sum of the powers of the variables is the same on each side of the equation.<\/p>\n<p>The general form of a linear first-order differential equation is:<\/p>\n<p>y'(x) = a(x)y(x) + b(x)<\/p>\n<p>Where:<\/p>\n<p>y'(x) is the derivative of y(x)<\/p>\n<p>a(x) is a constant<\/p>\n<p>b(x) is a constant<\/p>\n<h2><span class=\"ez-toc-section\" id=\"First_Order_Linear_Differential_Equation\"><\/span>First Order Linear Differential Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A first order linear differential equation is an equation in which the first derivative of a function is linear in the function&#8217;s argument. A first order linear differential equation typically has the form:<\/p>\n<p>,<\/p>\n<p>where is a function and is its first derivative.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Solve_1st_Order_Differential_Equations\"><\/span>How to Solve 1st Order Differential Equations?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are a few steps in solving 1st order differential equations:<\/p>\n<p>1. Assume a particular solution to the equation.<\/p>\n<p>2. Use algebra to solve for the particular solution.<\/p>\n<p>3. Check the solution by plugging it back into the differential equation.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solving_1st_order_differential_equations_can_be_tedious_but_the_two_approaches_mentioned_below_can_ease_things_out\"><\/span>Solving 1st order differential equations can be tedious but the two approaches mentioned below can ease things out.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Solution using Separation of Variables<\/p>\n<p>This is the most common technique for solving 1st order linear differential equations. The idea is to divide the equation into two parts \u2013 one that contains only the derivatives and one that contains only the constants. This can be done by multiplying both sides of the equation by a common factor if needed.<\/p>\n<p>After the equation has been divided, the two parts can be solved separately.<\/p>\n<p>Here is an example:<\/p>\n<p>The equation is:<\/p>\n<p>The equation can be divided by y to get:<\/p>\n<p>The equation can be divided by x to get:<\/p>\n<p>The two parts can now be solved separately.<\/p>\n<p>The derivative part can be solved using the Product Rule:<\/p>\n<p>The constant part can be solved using the Quadratic Formula:<\/p>\n<p>The final solution is:<\/p>\n<p>Solution using Integration<\/p>\n<p>This approach is useful when the differential equation cannot be solved using separation of variables.<\/p>\n<p>The first step is to integrate both sides of the equation. After integration, the equation will look like an algebraic equation.<\/p>\n<p>Next, solve the algebraic equation.<\/p>\n<p>Here is an example:<\/p>\n<p>The equation is:<\/p>\n<p>The equation can be integrated to get:<\/p>\n<p>After integration, the equation becomes an algebraic equation.<\/p>\n<p>Next, solve the algebraic equation.<\/p>\n<p>The solution is:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Explain in Detail :General Solution of 1st Order Differential Equation A first-order differential equation is an equation that describes the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"First Order Differential Equation","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about First Order Differential Equation topic of Maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/first-order-differential-equation\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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