{"id":13575,"date":"2023-05-02T10:00:31","date_gmt":"2023-05-02T04:30:31","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13575"},"modified":"2023-05-03T09:44:21","modified_gmt":"2023-05-03T04:14:21","slug":"differential-equations","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/differential-equations\/","title":{"rendered":"Differential Equations"},"content":{"rendered":"<h2>Differential Equations<\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/v8n8Na-WDrI?list=PLbYOkEbzW902GJZswbMnWHQaP4kKMS2TV\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>An equation involving independent variable x, dependent variable y and the differential coefficients \\(\\frac { dy }{ dx } ,\\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ,&#8230;..\\)\u00a0is called differential equation.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129131\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg\" alt=\"Differential Equations 1\" width=\"561\" height=\"137\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg 561w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1-300x73.jpg 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p><strong>(1) Order of a differential equation:<\/strong><br \/>\nThe order of a differential equation is the order of the highest derivative occurring in the differential equation. For example, the order of above differential equations are 1,1,4 and 2 respectively.<br \/>\nThe order of a differential equation is a positive integer. To determine the order of a differential equation, it is not needed to make the equation free from radicals.<\/p>\n<p><strong>(2) Degree of a differential equation:<\/strong><br \/>\nThe degree of a differential equation is the degree of the highest order derivative, when differential coefficients are made free from radicals and fractions. The degree of above differential equations are 1, 1, 3 and 2 respectively.<\/p>\n<h3>Formation of differential equation<\/h3>\n<p>Formulating a differential equation from a given equation representing a family of curves means finding a differential equation whose solution is the given equation. The equation so obtained is the differential equation of order n for the family of given curves.<\/p>\n<p><strong>Algorithm for formation of differential equations<\/strong><\/p>\n<p><strong>Step (i):<\/strong> Write the given equation involving independent variable x (say), dependent variable y (say) and the arbitrary constants.<br \/>\n<strong>Step (ii):<\/strong> Obtain the number of arbitrary constants in step (i). Let there be n arbitrary constants.<br \/>\n<strong>Step (iii):<\/strong> Differentiate the relation in step (i) n times with respect to x.<br \/>\n<strong>Step (iv):<\/strong> Eliminate arbitrary constants with the help of n equations involving differential coefficients obtained in step (iii) and an equation in step (i). The equation so obtained is the desired differential equation.<\/p>\n<h3>Variable separable type differential equation<\/h3>\n<p><strong>(1) Equations in variable separable form:<\/strong><br \/>\nIf the differential equation of the form <em>f<sub>1<\/sub>(x) dx = f<sub>2<\/sub>(y) dy<\/em> \u00a0 &#8230;..(i)<br \/>\nwhere <em>f<sub>1<\/sub><\/em>\u00a0and <em>f<sub>2<\/sub><\/em>\u00a0being functions of x and y only. Then we say that the variables are separable in the differential equation.<br \/>\nThus, integrating both sides of (i), we get its solution as <em>\u222bf<sub>1<\/sub>(x) dx = \u222bf<sub>2<\/sub>(y) dy + c<\/em>, where c is an arbitrary constant.<br \/>\nThere is no need of introducing arbitrary constants to both sides as they can be combined together to give just one.<\/p>\n<p><strong>(2) Equations reducible to variable separable form:<\/strong><br \/>\n(i) Differential equations of the form \\(\\frac { dy }{ dx } =f(ax+by+c)\\)\u00a0can be reduced to variable separable form by the substitution <em>ax + by + c = Z<\/em>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129132\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-2.jpg\" alt=\"Differential Equations 2\" width=\"544\" height=\"61\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-2.jpg 544w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-2-300x34.jpg 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\n(ii) Differential equation of the form<br \/>\nThis is variable separable form and can be solved.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129133\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-3.jpg\" alt=\"Differential Equations 3\" width=\"453\" height=\"242\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-3.jpg 453w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-3-300x160.jpg 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<h3><a href=\"https:\/\/www.aplustopper.com\/homogeneous-differential-equations\/\">Homogeneous differential equation<\/a><\/h3>\n<h3>Exact differential equation<\/h3>\n<p><strong>(1) Exact differential equation:<\/strong><br \/>\nIf M and N are functions of x and y, the equation <em>Mdx + Ndy = 0<\/em> is called exact when there exists a function f(x, y) of x and y such that<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129135\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-4.jpg\" alt=\"Differential Equations 4\" width=\"605\" height=\"291\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-4.jpg 605w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-4-300x144.jpg 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><br \/>\nAn exact differential equation can always be derived from its general solution directly by differentiation without any subsequent multiplication, elimination etc.<\/p>\n<p><strong>(2) Integrating factor:<\/strong><br \/>\nIf an equation of the form <em>Mdx + Ndy = 0<\/em> is not exact, it can always be made exact by multiplying by some function of x and y. Such a multiplier is called an integrating factor.<\/p>\n<p><strong>(3) Working rule for solving an exact differential equation:<\/strong><br \/>\n<strong>Step (i):<\/strong> Compare the given equation with <em>Mdx + Ndy = 0<\/em> and find out <em>M<\/em> and <em>N<\/em>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129136\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-5.jpg\" alt=\"Differential Equations 5\" width=\"598\" height=\"85\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-5.jpg 598w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-5-300x43.jpg 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><br \/>\n<strong>Step (ii):<\/strong> Integrate <em>M<\/em> with respect to x treating y as a constant.<br \/>\n<strong>Step (iii):<\/strong> Integrate <em>N<\/em> with respect to y treating x as constant and omit those terms which have been already obtained by integrating M.<br \/>\n<strong>Step (iv):<\/strong> On adding the terms obtained in steps (ii) and (iii) and equating to an arbitrary constant, we get the required solution.<br \/>\nIn other words, solution of an exact differential equation is<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129137\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-6.jpg\" alt=\"Differential Equations 6\" width=\"244\" height=\"86\" \/><\/p>\n<h3>Solution by inspection<\/h3>\n<p>If we can write the differential equation in the form <em>f(f<sub>1<\/sub>(x))d(f<sub>1<\/sub>(x, y)) + \u03d5(f<sub>2<\/sub>(x))d(f<sub>2<\/sub>(x, y)) + \u2026\u2026\u2026. = 0<\/em>, then each term can be easily integrated separately. For this the following results must be memorized.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129138\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-7.jpg\" alt=\"Differential Equations 7\" width=\"404\" height=\"856\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-7.jpg 404w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-7-142x300.jpg 142w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129139\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-8.jpg\" alt=\"Differential Equations 8\" width=\"414\" height=\"551\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-8.jpg 414w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-8-225x300.jpg 225w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<h3><a href=\"https:\/\/www.aplustopper.com\/solution-first-order-linear-differential-equations\/\">Linear differential equation<\/a><\/h3>\n<h3>Application of differential equation<\/h3>\n<p>Differential equation is applied in various practical fields of life. It is used to define various physical laws and quantities. It is widely used in physics, chemistry, engineering etc.<br \/>\nSome important fields of application are:<br \/>\n(i) Rate of change (ii) Geometrical problems etc.<\/p>\n<h3>Miscellaneous differential equation<\/h3>\n<p>A special type of second order differential equation:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129140\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-9.jpg\" alt=\"Differential Equations 9\" width=\"540\" height=\"536\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-9.jpg 540w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-9-150x150.jpg 150w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-9-300x298.jpg 300w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-9-100x100.jpg 100w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Differential Equations An equation involving independent variable x, dependent variable y and the differential coefficients \u00a0is called differential equation. (1) Order of a differential equation: The order of a differential equation is the order of the highest derivative occurring in the differential equation. For example, the order of above differential equations are 1,1,4 and 2 [&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":[5034,5031,5037,5038,5008,5035,5033,5032,5036,5030],"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>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\/differential-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differential Equations\" \/>\n<meta property=\"og:description\" content=\"Differential Equations An equation involving independent variable x, dependent variable y and the differential coefficients \u00a0is called differential equation. (1) Order of a differential equation: The order of a differential equation is the order of the highest derivative occurring in the differential equation. For example, the order of above differential equations are 1,1,4 and 2 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.aplustopper.com\/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=\"2023-05-02T04:30:31+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-05-03T04:14:21+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/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=\"4 minutes\" \/>\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\/differential-equations\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg\",\"width\":561,\"height\":137,\"caption\":\"Differential Equations 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#webpage\",\"url\":\"https:\/\/www.aplustopper.com\/differential-equations\/\",\"name\":\"Differential Equations - A Plus Topper\",\"isPartOf\":{\"@id\":\"https:\/\/www.aplustopper.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#primaryimage\"},\"datePublished\":\"2023-05-02T04:30:31+00:00\",\"dateModified\":\"2023-05-03T04:14:21+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.aplustopper.com\/differential-equations\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.aplustopper.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Differential Equations\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#webpage\"},\"author\":{\"@id\":\"https:\/\/www.aplustopper.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794\"},\"headline\":\"Differential Equations\",\"datePublished\":\"2023-05-02T04:30:31+00:00\",\"dateModified\":\"2023-05-03T04:14:21+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#webpage\"},\"wordCount\":717,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/differential-equations\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg\",\"keywords\":[\"Application of differential equation\",\"Degree of a differential equation\",\"Exact differential equation\",\"Formation of differential equation\",\"Homogeneous differential equation\",\"Linear differential equation\",\"Miscellaneous differential equation\",\"Order of a differential equation\",\"Solution by inspection\",\"Variable separable type differential equation\"],\"articleSection\":[\"Mathematics\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.aplustopper.com\/differential-equations\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.aplustopper.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/www.aplustopper.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Differential Equations - A Plus Topper","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.aplustopper.com\/differential-equations\/","og_locale":"en_US","og_type":"article","og_title":"Differential Equations","og_description":"Differential Equations An equation involving independent variable x, dependent variable y and the differential coefficients \u00a0is called differential equation. (1) Order of a differential equation: The order of a differential equation is the order of the highest derivative occurring in the differential equation. For example, the order of above differential equations are 1,1,4 and 2 [&hellip;]","og_url":"https:\/\/www.aplustopper.com\/differential-equations\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2023-05-02T04:30:31+00:00","article_modified_time":"2023-05-03T04:14:21+00:00","og_image":[{"url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg"}],"twitter_card":"summary","twitter_misc":{"Written by":"Prasanna","Est. reading time":"4 minutes"},"schema":{"@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\/differential-equations\/#primaryimage","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg","width":561,"height":137,"caption":"Differential Equations 1"},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/differential-equations\/#webpage","url":"https:\/\/www.aplustopper.com\/differential-equations\/","name":"Differential Equations - A Plus Topper","isPartOf":{"@id":"https:\/\/www.aplustopper.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.aplustopper.com\/differential-equations\/#primaryimage"},"datePublished":"2023-05-02T04:30:31+00:00","dateModified":"2023-05-03T04:14:21+00:00","breadcrumb":{"@id":"https:\/\/www.aplustopper.com\/differential-equations\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.aplustopper.com\/differential-equations\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.aplustopper.com\/differential-equations\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.aplustopper.com\/"},{"@type":"ListItem","position":2,"name":"Differential Equations"}]},{"@type":"Article","@id":"https:\/\/www.aplustopper.com\/differential-equations\/#article","isPartOf":{"@id":"https:\/\/www.aplustopper.com\/differential-equations\/#webpage"},"author":{"@id":"https:\/\/www.aplustopper.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794"},"headline":"Differential Equations","datePublished":"2023-05-02T04:30:31+00:00","dateModified":"2023-05-03T04:14:21+00:00","mainEntityOfPage":{"@id":"https:\/\/www.aplustopper.com\/differential-equations\/#webpage"},"wordCount":717,"commentCount":0,"publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"image":{"@id":"https:\/\/www.aplustopper.com\/differential-equations\/#primaryimage"},"thumbnailUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Differential-Equations-1.jpg","keywords":["Application of differential equation","Degree of a differential equation","Exact differential equation","Formation of differential equation","Homogeneous differential equation","Linear differential equation","Miscellaneous differential equation","Order of a differential equation","Solution by inspection","Variable separable type differential equation"],"articleSection":["Mathematics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.aplustopper.com\/differential-equations\/#respond"]}]},{"@type":"Person","@id":"https:\/\/www.aplustopper.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/www.aplustopper.com\/author\/prasanna\/"}]}},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/13575"}],"collection":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/comments?post=13575"}],"version-history":[{"count":1,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/13575\/revisions"}],"predecessor-version":[{"id":159222,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/posts\/13575\/revisions\/159222"}],"wp:attachment":[{"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/media?parent=13575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/categories?post=13575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aplustopper.com\/wp-json\/wp\/v2\/tags?post=13575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}