{"id":57800,"date":"2021-10-11T01:32:32","date_gmt":"2021-10-11T01:32:32","guid":{"rendered":"https:\/\/papersspot.com\/blog\/2021\/10\/11\/project-mth-reduction-of-order\/"},"modified":"2021-10-11T01:32:32","modified_gmt":"2021-10-11T01:32:32","slug":"project-mth-reduction-of-order","status":"publish","type":"post","link":"https:\/\/papersspot.com\/blog\/2021\/10\/11\/project-mth-reduction-of-order\/","title":{"rendered":"Project MTH. Reduction of Order"},"content":{"rendered":"<p>Assume thatpandqare continuous onIfunctions. If you know two linearlyindependent solutions to this linear equation then you can write t he general solution astheir linear combination. Therefore you are interested in finding another solution which islinearly independent fromy1. You can accomplish this by using a method that is calledReduction of Order. Seek the second solutiony2in the formy2(x) =v(x)y1(x), where youdo not knowv(x). Substitutey2in the equation, thus obtaining a second order, reducibleequation forv. This equation you can solve by a substitutionz=v\u2032. Findz, then integrateit to findv. Then observe that the expression fory2contains a linear summand ofy1. Theleftover is the second, simple, linear independent ofy1solution of the original <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Assume thatpandqare continuous onIfunctions. If you know two linearlyindependent solutions to this linear equation then you can write t he general solution astheir linear combination. Therefore you are interested in finding another solution which islinearly independent fromy1. You can accomplish this by using a method that is calledReduction of Order. Seek the second solutiony2in the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[12],"class_list":["post-57800","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-religion-and-theology"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/57800","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=57800"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/57800\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=57800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=57800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=57800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}