{"id":4347,"date":"2022-06-11T08:16:58","date_gmt":"2022-06-11T08:16:58","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4347"},"modified":"2022-06-11T08:16:58","modified_gmt":"2022-06-11T08:16:58","slug":"formation-of-differential-equations","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/11\/formation-of-differential-equations\/","title":{"rendered":"Formation of Differential Equations"},"content":{"rendered":"\n<p>The differential equations are modeled from real-life scenarios.<\/p>\n\n\n\n<ul><li>Newton&#8217;s second law is described by the differential equation <\/li><\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>m d<sup>2<\/sup>h \/ dh<sup>2<\/sup> = f(t,h(t), dh \/ dt)<\/code><\/pre>\n\n\n\n<ul><li>where m is the mass of the object, h is the height above the ground level. This is the second-order differential equation of the unknown height as a function of time.<\/li><li>As time increases, the population increases. If r > 0 is the growth rate, then the differential equation modeling the population is given as dN\/dt = rN.<\/li><li>The rate at which the disease spreads is proportional to the product of the infected people with the non-infected people. This is modeled as dN\/ DT = k N(T-N), where T is the fixed population and N is the number of people affected by the disease.<\/li><li>For a certain substance, the rate of change of vapor pressure P with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature. dP\/dt = k P\/T^2<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The differential equations are modeled from real-life scenarios. Newton&#8217;s second law is described by the differential equation where m is the mass of the object, h is the height above the ground level. This is the second-order differential equation of the unknown height as a function of time. As time increases, the population increases. If [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[766],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4347"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4347"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4347\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}