{"id":2919,"date":"2021-07-12T21:08:30","date_gmt":"2021-07-12T15:38:30","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=2919"},"modified":"2026-01-12T16:27:48","modified_gmt":"2026-01-12T10:57:48","slug":"how-to-solve-a-differential-equation","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/how-to-solve-a-differential-equation\/","title":{"rendered":"How to solve a differential equation?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Overvie<\/strong>w<\/h2>\n\n\n\n<p>A differential equation is an equation consists differential co-efficient.<\/p>\n\n\n\n<p>For example-<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"79\" height=\"41\" src=\"https:\/\/lh3.googleusercontent.com\/_LIhWgtHcZf_tFM08eKy4sEwTUm7IGWh2D5UyXRfmt7N8ywumBi1b4Wi19Tq9DUvmJS1DPL4c2EliVmcaR0ZoKO6I00aeeQethXndlnCQ2azxj9LOzfXbOlecl8FIqF5bVwbbCpp\">&nbsp; is the DE.<\/p>\n\n\n\n<p>There are two types of differential equations-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/eiiX1rJxkskERN8dNGDVPCwGdT6GhcjmjN0LryEGJq27k7_uVcFjUrcls0xAi7I6RSBbtCG0YrRipDE9f-u-3ICTfwsY9V5w3q3qjTX92Gg8JQMTdXQrTtBv2RYgpkWENm1AcJdK\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>Ordinary DE<\/strong><\/p>\n\n\n\n<p>When a DE consists derivatives with respect to a single independent variable, we call it an ordinary DE.<\/p>\n\n\n\n<p><strong>Partial<\/strong> <strong>DE<\/strong><\/p>\n\n\n\n<p>When a DE consisting partial derivatives with respect to more than one independent variable, we call it a partial DE.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Order and degree of differential equation<\/h2>\n\n\n\n<p>The order of the highest differential co-efficient present in the equation is known as the order of a DE.<\/p>\n\n\n\n<p>Degree of a DE is the degree of the highest ordered derivative (when the derivatives are cleared of radicals and fractions).<\/p>\n\n\n\n<p><strong>Note<\/strong>: we form a DE by differentiating the ordinary equation and eliminating the arbitrary constants.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Differential equation introduction | First order differential equations | Khan Academy\" width=\"1170\" height=\"658\" src=\"https:\/\/www.youtube.com\/embed\/6o7b9yyhH7k?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution of a differential equation<\/h2>\n\n\n\n<p>An equation with dependent variable (y) and independent variable (x) and does not contain derivative, which satisfies the DE, is called the solution of the DE.<\/p>\n\n\n\n<p>Here we will discuss the solution of differential equations with variable separable.<\/p>\n\n\n\n<p>If a DE is<\/p>\n\n\n\n<p class=\"has-text-align-center\">f(y)dy = g(x) dx<\/p>\n\n\n\n<p>Which means, variable are separable, then we can get the solution by using integration.<\/p>\n\n\n\n<p><strong>Steps-<\/strong><\/p>\n\n\n\n<p>The following steps we follow to find the solution of a differential equation-<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>First we separate the variables such as &#8211; f(y)dy = g(x) dx.<\/li>\n\n\n\n<li>Now we use integration on both sides-<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/3splQeM2uK8jhIAgPGn3M8LAAK7GIJFtzx142zI3GW9tzruXlce_f3J-EcEkQRiXIVLOBvDY6Nu_zrrX5Q_-K6CpOJ-G8bmp84TdTOcdfCY4n2aKbq8Ic3VV6lDeK-pT167QNm8x\" alt=\"\"\/><\/figure><\/div>\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li>Then finally we add constant C on right hand side.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solved examples<\/strong><\/h2>\n\n\n\n<p><strong>Example: Solve the following DE.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/BNwzrZweF9xas0lpOgEy748LgG1dL_lunzrN0rd3FxdmfIQdefwt8ZPLoKW7v2sm3liGKisqKik79EDfnF9sDSqw4yYJbVNEquJg8agkNhntlTKu1axrPOiw6NG9HJAyuDCW6H6C\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Solution:<\/p>\n\n\n\n<p>Here we have-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Et2n32k0gaGdHHzM1RemFbibJHTdWIqKzStYi1QzDn54lfh15qTNZ81X2VvnA1C1cCRbPdVUPh54PecCC-6iNgWieKNyvurl1l55fMmIv_ZbWgke7JSysRcvBqwYXr7W2prQSqLc\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Now separating the variables, we get-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/wllK_6f8DMmxrVbyju5bx54r5WA0d-yha2sWpsFBGeFdulziG2LmMj_DZG7Ls21QD6rjEbEg5gMU6YlrG6tnYn4CjSi7h5rzeUJZmlzxoPIc49NNPd7UiPoKsRpMdTAdXf7Nj-gh\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>then we integrate both sides-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/_xgAn05txlrk4NW_qWIdA7aYpUodDK17gNQQKbH-nkueXNdoZdfm5AXaCaMs3kcNYs2mjYbad36kTGNZ6MRl1yGzGnoFAF3CIbjCTo4Kv8iMtj_OGXo1s6Tw62fSGMB7qjl-qeJz\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>We get-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/vpVWiNC4JaC1GCPnYPbS0F142DzmlTZZuDnD7eoNMxl7skogNS_hJIRxBHroRv9z3m2-sdW-e1yaiBHwEefAPv9DIBd7oSX83j9fzNIg4MF94K6PCl97U_6TAH1e8e-P_ka2DGlG\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Here C is constant.<\/p>\n\n\n\n<p><strong>Example: Solve the DE-<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/YYzjkXsbT3pxjnVeM4lgGdap9_rYHlwWCk_hF-0Tg3EsaSrvx1WPAY2St-1uKLU3pMB4y5ouB3T-T2JBjFvO3BJHQPzVhI8ZrSyFovAdgWOCGlbdn1uQvWKr6mJdi7Q_zazq74r8\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Solution-<\/p>\n\n\n\n<p>Here we have-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/uilOBEBMJy9lr7b4tnZz9C9AEDt6QgtJNnkZ4ED1OLgse0ndQnaCiYCNOh-BY6SSCJWdnsgtgXz-QUGRDXd3WKu_U1z8aJZCAjwl-36c1blQROQu-3vFKSIF0K0LfFeF5U9-xn2M\" alt=\"\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/rvvIVMvAwjvd31O_Bcf52Ad3oNFPKh-QaML1j_AeDGvd3iDatZedpbPy4KMP7pNof4gq07U_4mJBTBHc6Et7adNIbreWDdYQenAuw6DPk_YJQMliqpw56rSNQOuWFavvmH0khNzb\" alt=\"\"\/><\/figure>\n\n\n\n<p>Now separating the variables, we get-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/ZuS_5aUCeHYaYG6raVeASeib2WdbJRexApBQ2ebadNP6s6PP5WUDeDYNDeAbVGOBQHxcr9bFAD41XLTzF87S4v-JnosSq6Q7FigiAjBmRcIL2ZaTW5w2YMlXxoD6BtnutHWcp2ZU\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Integrate both sides-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/bLgqCkA4Rk3tLwRdMpxruCiJEg0O7n74wx5xKoxNvtj0_dZVlIlAFV3OmVR4P3D6WkdA488PDlZzKeM7RTfLjFYDt-bozOt4g7vCPh-QGF3Fm3e6QOr0GX6Xf8iYc8RPZRuVZi_y\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Replace the value of v,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/f3H7xmrdh0AFBpPvoDaIpUGHxdtKLV_ajZhdwJklqxpKrYQV5PWnidHhbR_k4fGIGa8RIQZuQeHfUj2ZP2fipQlYbug1UE0tfqaXUqjNOLwYwKwTU8MNR8YHvr_p3ZqMKZFJhzFw\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-taylors-series\" target=\"_blank\" rel=\"noreferrer noopener\">What is Taylor&#8217;s series?<\/a> <a href=\"https:\/\/admin.gpeijabar.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/admin.gpeijabar.org\/<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>An equation consisting differential co-efficient is called a differential equation. There are two types of differential equations.<\/p>\n","protected":false},"author":3,"featured_media":2994,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-2919","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to solve a differential equation? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"An equation consisting differential co-efficient is called a differential equation. 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