{"id":133960,"date":"2023-03-12T17:33:04","date_gmt":"2023-03-12T12:03:04","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133960"},"modified":"2023-03-12T17:33:04","modified_gmt":"2023-03-12T12:03:04","slug":"show-that-x2-y2-die-2xy-dy-0-is-a-differential-equation-of-the-type-dy-dx-gy-x","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/show-that-x2-y2-die-2xy-dy-0-is-a-differential-equation-of-the-type-dy-dx-gy-x","title":{"rendered":"Show that (x2 -y2) die + 2xy dy = 0 is a differential equation of the type dy\/dx =g(y\/x)."},"content":{"rendered":"<h2>Question: Show that (x2 -y2) die + 2xy dy = 0 is a differential equation of the type dy\/dx =g(y\/x).<\/h2>\n<p>&nbsp;<\/p>\n<h3>The correct answer is &#8211;<\/h3>\n<h4>To show that (x2 &#8211; y2) dy + 2xy dx = 0 is a differential equation of the type dy\/dx = g(y\/x), we can make the substitution y = vx, which gives us dy\/dx = v + x (dv\/dx). We can also express x in terms of v and y as x = y\/v. Substituting these values in the given equation, we get:<\/h4>\n<h4>(x2 &#8211; y2) dy + 2xy dx = 0 (x2 &#8211; v2x2) (v dx) + 2y (y\/v) dx = 0 (x2 &#8211; v2x2) v + 2y (y\/v) (dv\/dx) = 0 (v2 &#8211; 1) x2 dv + 2y2 v dv = 0<\/h4>\n<h4>Dividing both sides by x2v, we get:<\/h4>\n<h4>(v2 &#8211; 1) dv + 2(v\/y) dv = 0<\/h4>\n<h4>This is a differential equation of the type dy\/dx = g(y\/x), where g(y\/x) = -2(y\/x)\/ (1 &#8211; (y\/x)2).<\/h4>\n","protected":false},"excerpt":{"rendered":"<p>Question: Show that (x2 -y2) die + 2xy dy = 0 is a differential equation of the type dy\/dx =g(y\/x). &nbsp; The correct answer is &#8211; To show that (x2 &#8211; y2) dy + 2xy dx = 0 is a differential equation of the type dy\/dx = g(y\/x), we can make the substitution y = [&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-133960","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\/133960","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=133960"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133960\/revisions"}],"predecessor-version":[{"id":133961,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133960\/revisions\/133961"}],"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=133960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}