{"id":133962,"date":"2023-03-12T17:36:21","date_gmt":"2023-03-12T12:06:21","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133962"},"modified":"2023-03-12T17:36:21","modified_gmt":"2023-03-12T12:06:21","slug":"solve-the-above-equation-to-find-its-general-solution","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/solve-the-above-equation-to-find-its-general-solution","title":{"rendered":"Solve the above equation to find its general solution."},"content":{"rendered":"<h2>Question: Solve the above equation to find its general solution.<\/h2>\n<p>&nbsp;<\/p>\n<h3>The correct answer is &#8211;<\/h3>\n<h4>To solve the above equation, we need to separate the variables v and x. Dividing both sides by (v2 &#8211; 1), we get:<\/h4>\n<h4>dv\/dx + (2v\/y)\/(v2 &#8211; 1) = 0<\/h4>\n<h4>Multiplying both sides by (1\/v), we get:<\/h4>\n<h4>(1\/v) dv\/dx + (2\/y) \/ (v2 &#8211; 1) = 0<\/h4>\n<h4>Substituting u = 1\/v, we get:<\/h4>\n<h4>du\/dx &#8211; (2\/y)\/(1 &#8211; u2) = 0<\/h4>\n<h4>Separating the variables u and x, we get:<\/h4>\n<h4>\u222b (1 &#8211; u2) du = \u222b (2\/y) dx<\/h4>\n<h4>Solving the integrals, we get:<\/h4>\n<h4>u = c1 cos(x\/c2) v = 1\/u = c2\/(c1 cos(x\/c2)) y = vx = c2x\/(c1 cos(x\/c2))<\/h4>\n<h4>Therefore, the general solution of the given differential equation is y = (c2\/c1) x sec(x\/c2)<\/h4>\n","protected":false},"excerpt":{"rendered":"<p>Question: Solve the above equation to find its general solution. &nbsp; The correct answer is &#8211; To solve the above equation, we need to separate the variables v and x. Dividing both sides by (v2 &#8211; 1), we get: dv\/dx + (2v\/y)\/(v2 &#8211; 1) = 0 Multiplying both sides by (1\/v), we get: (1\/v) dv\/dx [&hellip;]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-133962","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133962","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=133962"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133962\/revisions"}],"predecessor-version":[{"id":133963,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133962\/revisions\/133963"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=133962"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133962"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}