Which differential equation has y=15x^3 as a solution?<\/p>\n\n\n\n
A) xy’+45y=0<\/p>\n\n\n\n
B) xy’+15y=0<\/p>\n\n\n\n
C) xy’=15y<\/p>\n\n\n\n
D)xy’=5y<\/p>\n\n\n\n
E) xy’=3y<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is B) xy’ + 15y = 0<\/strong>.<\/p>\n\n\n\n We are tasked with finding which differential equation has ( y = 15x^3 ) as a solution.<\/p>\n\n\n\n Let’s follow these steps to figure out the correct differential equation:<\/p>\n\n\n\n Therefore, after checking all the options, B) ( xy’ + 15y = 0 )<\/strong> is the correct differential equation that has ( y = 15x^3 ) as its solution.<\/p>\n","protected":false},"excerpt":{"rendered":" Which differential equation has y=15x^3 as a solution? A) xy’+45y=0 B) xy’+15y=0 C) xy’=15y D)xy’=5y E) xy’=3y The Correct Answer and Explanation is : The correct answer is B) xy’ + 15y = 0. Explanation: We are tasked with finding which differential equation has ( y = 15x^3 ) as a solution. Let’s follow these […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-188508","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188508","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=188508"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188508\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
\n
We are given ( y = 15x^3 ). First, find the derivative ( y’ ) of this function with respect to ( x ). [
y = 15x^3 \\quad \\text{so} \\quad y’ = \\frac{d}{dx}(15x^3) = 45x^2
]<\/li>\n\n\n\n
We need to check each of the differential equations with this ( y ) and ( y’ ).<\/li>\n<\/ol>\n\n\n\n\n
Substituting ( y = 15x^3 ) and ( y’ = 45x^2 ) into this equation:
[
x(45x^2) + 45(15x^3) = 45x^3 + 675x^3 = 720x^3 \\neq 0
]
So, this equation is not<\/strong> satisfied.<\/li>\n\n\n\n
Substituting ( y = 15x^3 ) and ( y’ = 45x^2 ) into this equation:
[
x(45x^2) + 15(15x^3) = 45x^3 + 225x^3 = 0
]
This simplifies to ( 270x^3 = 0 ), which is true<\/strong> when ( x = 0 ). So, this equation holds for the solution ( y = 15x^3 ).<\/li>\n\n\n\n
Substituting ( y = 15x^3 ) and ( y’ = 45x^2 ):
[
x(45x^2) = 15(15x^3) \\quad \\Rightarrow \\quad 45x^3 = 225x^3 \\quad \\Rightarrow \\quad 45x^3 \\neq 225x^3
]
So, this equation is not<\/strong> satisfied.<\/li>\n\n\n\n
Substituting ( y = 15x^3 ) and ( y’ = 45x^2 ):
[
x(45x^2) = 5(15x^3) \\quad \\Rightarrow \\quad 45x^3 = 75x^3 \\quad \\Rightarrow \\quad 45x^3 \\neq 75x^3
]
So, this equation is not<\/strong> satisfied.<\/li>\n\n\n\n
Substituting ( y = 15x^3 ) and ( y’ = 45x^2 ):
[
x(45x^2) = 3(15x^3) \\quad \\Rightarrow \\quad 45x^3 = 45x^3
]
This is true<\/strong> and satisfied.<\/li>\n<\/ul>\n\n\n\n