{"id":13549,"date":"2020-12-10T06:39:12","date_gmt":"2020-12-10T01:09:12","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13549"},"modified":"2020-12-10T12:00:51","modified_gmt":"2020-12-10T06:30:51","slug":"homogeneous-differential-equations","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/homogeneous-differential-equations\/","title":{"rendered":"Homogeneous Differential Equations"},"content":{"rendered":"<h2>Homogeneous Differential Equations<\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/uSvaMdZjgd8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h3>Homogeneous <a href=\"https:\/\/www.aplustopper.com\/differential-equations\/\">differential equation<\/a><\/h3>\n<p>A function f(x,y) is called a homogeneous function of degree if f(\u03bbx, \u03bby) = \u03bb<sup>n <\/sup>f(x, y).<br \/>\nFor example, f(x, y) = x<sup>2<\/sup> \u2013 y<sup>2<\/sup> + 3xy\u00a0is a homogeneous function of degree 2.<\/p>\n<p>A homogenous function of degree n can always be written as<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129004\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-1.jpg\" alt=\"Homogeneous Differential Equations 1\" width=\"328\" height=\"66\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-1.jpg 328w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-1-300x60.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>If a first-order first-degree differential equation is expressible in the form \\(\\frac { dy }{ dx } =\\frac { f(x,y) }{ g(x,y) }\\)\u00a0where f(x, y) and g(x, y) are homogeneous functions of the same degree, then it is called a homogeneous differential equation. Such type of equations can be reduced to variable separable form by the substitution y = \u03bdx. The given differential equation can be written as<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129005\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-2.jpg\" alt=\"Homogeneous Differential Equations 2\" width=\"598\" height=\"186\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-2.jpg 598w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-2-300x93.jpg 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>On integration, \\(\\int { \\frac { 1 }{ F(v)-v } \u00a0} dv\\quad =\\quad \\int { \\frac { dx }{ x } +c }\\) where c is an arbitrary constant of integration. After integration, v will be replaced by \\(\\frac { y }{ x }\\)\u00a0in complete solution.<\/p>\n<h3><strong>Equation reducible to homogeneous form<\/strong><\/h3>\n<p>A first order, first degree differential equation of the form<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129006\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-3.jpg\" alt=\"Homogeneous Differential Equations 3\" width=\"332\" height=\"66\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-3.jpg 332w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-3-300x60.jpg 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nThis is non-homogeneous.<br \/>\nIt can be reduced to homogeneous form by certain substitutions. Put x = X + h, y = Y + k.<br \/>\nWhere h and k are constants, which are to be determined.<\/p>\n<h3>Homogeneous <a href=\"https:\/\/www.aplustopper.com\/differential-equations\/\">Differential Equations<\/a> Problems with Solutions<\/h3>\n<p><strong>1.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129007\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-4.jpg\" alt=\"Homogeneous Differential Equations 4\" width=\"539\" height=\"87\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-4.jpg 539w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-4-300x48.jpg 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129009\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-5.jpg\" alt=\"Homogeneous Differential Equations 5\" width=\"504\" height=\"440\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-5.jpg 504w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-5-300x262.jpg 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<strong>2.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129010\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-6.jpg\" alt=\"Homogeneous Differential Equations 6\" width=\"489\" height=\"57\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-6.jpg 489w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-6-300x35.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129011\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-7.jpg\" alt=\"Homogeneous Differential Equations 7\" width=\"424\" height=\"286\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-7.jpg 424w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-7-300x202.jpg 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><br \/>\n<strong>3.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129012\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-8.jpg\" alt=\"Homogeneous Differential Equations 8\" width=\"409\" height=\"60\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-8.jpg 409w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-8-300x44.jpg 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129013\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-9.jpg\" alt=\"Homogeneous Differential Equations 9\" width=\"420\" height=\"601\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-9.jpg 420w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-9-210x300.jpg 210w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><br \/>\n<strong>4.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129014\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-10.jpg\" alt=\"Homogeneous Differential Equations 10\" width=\"543\" height=\"61\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-10.jpg 543w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-10-300x34.jpg 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129015\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-11.jpg\" alt=\"Homogeneous Differential Equations 11\" width=\"505\" height=\"588\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-11.jpg 505w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-11-258x300.jpg 258w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><br \/>\n<strong>5.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129016\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-12.jpg\" alt=\"Homogeneous Differential Equations 12\" width=\"540\" height=\"60\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-12.jpg 540w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-12-300x33.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129017\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-13.jpg\" alt=\"Homogeneous Differential Equations 13\" width=\"504\" height=\"397\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-13.jpg 504w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-13-300x236.jpg 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<strong>6.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129031\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-14.jpg\" alt=\"Homogeneous Differential Equations 14\" width=\"505\" height=\"58\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-14.jpg 505w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-14-300x34.jpg 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129063\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-15.jpg\" alt=\"Homogeneous Differential Equations 15\" width=\"498\" height=\"469\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-15.jpg 498w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-15-300x283.jpg 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<strong>7.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129064\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-16.jpg\" alt=\"Homogeneous Differential Equations 16\" width=\"496\" height=\"59\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-16.jpg 496w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-16-300x36.jpg 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129065\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-17.jpg\" alt=\"Homogeneous Differential Equations 17\" width=\"460\" height=\"514\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-17.jpg 460w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-17-268x300.jpg 268w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><br \/>\n<strong>8.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129066\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-18.jpg\" alt=\"Homogeneous Differential Equations 18\" width=\"432\" height=\"58\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-18.jpg 432w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-18-300x40.jpg 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129067\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-19.jpg\" alt=\"Homogeneous Differential Equations 19\" width=\"504\" height=\"472\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-19.jpg 504w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-19-300x281.jpg 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<strong>9.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129068\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-20.jpg\" alt=\"Homogeneous Differential Equations 20\" width=\"456\" height=\"61\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-20.jpg 456w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-20-300x40.jpg 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129069\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-21.jpg\" alt=\"Homogeneous Differential Equations 21\" width=\"504\" height=\"334\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-21.jpg 504w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-21-300x199.jpg 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<strong>10.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129070\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-22.jpg\" alt=\"Homogeneous Differential Equations 22\" width=\"434\" height=\"59\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-22.jpg 434w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-22-300x41.jpg 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129071\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-23.jpg\" alt=\"Homogeneous Differential Equations 23\" width=\"453\" height=\"421\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-23.jpg 453w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-23-300x279.jpg 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><br \/>\n<strong>11.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129072\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-24.jpg\" alt=\"Homogeneous Differential Equations 24\" width=\"345\" height=\"55\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-24.jpg 345w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-24-300x48.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129073\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-25.jpg\" alt=\"Homogeneous Differential Equations 25\" width=\"476\" height=\"567\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-25.jpg 476w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-25-252x300.jpg 252w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\n<strong>12.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129074\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-26.jpg\" alt=\"Homogeneous Differential Equations 26\" width=\"537\" height=\"62\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-26.jpg 537w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-26-300x35.jpg 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129075\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-27.jpg\" alt=\"Homogeneous Differential Equations 27\" width=\"454\" height=\"809\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-27.jpg 454w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-27-168x300.jpg 168w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Homogeneous Differential Equations Homogeneous differential equation A function f(x,y) is called a homogeneous function of degree if f(\u03bbx, \u03bby) = \u03bbn f(x, y). For example, f(x, y) = x2 \u2013 y2 + 3xy\u00a0is a homogeneous function of degree 2. A homogenous function of degree n can always be written as If a first-order first-degree differential [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[5007,5008],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Homogeneous Differential Equations - A Plus Topper<\/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:\/\/www.aplustopper.com\/homogeneous-differential-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Homogeneous Differential Equations\" \/>\n<meta property=\"og:description\" content=\"Homogeneous Differential Equations Homogeneous differential equation A function f(x,y) is called a homogeneous function of degree if f(\u03bbx, \u03bby) = \u03bbn f(x, y). For example, f(x, y) = x2 \u2013 y2 + 3xy\u00a0is a homogeneous function of degree 2. A homogenous function of degree n can always be written as If a first-order first-degree differential [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.aplustopper.com\/homogeneous-differential-equations\/\" \/>\n<meta property=\"og:site_name\" content=\"A Plus Topper\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2020-12-10T01:09:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-12-10T06:30:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-1.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.aplustopper.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.aplustopper.com\/#website\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"name\":\"A Plus Topper\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.aplustopper.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/homogeneous-differential-equations\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-1.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Homogeneous-Differential-Equations-1.jpg\",\"width\":328,\"height\":66,\"caption\":\"Homogeneous Differential Equations 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.aplustopper.com\/homogeneous-differential-equations\/#webpage\",\"url\":\"https:\/\/www.aplustopper.com\/homogeneous-differential-equations\/\",\"name\":\"Homogeneous Differential Equations - 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For example, f(x, y) = x2 \u2013 y2 + 3xy\u00a0is a homogeneous function of degree 2. 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