Question

anyone here up for some differential equations?

Answer 1

yes

Answer 2

awesome....so i had a diff eq test this past friday. Few of us were talking about it afterwards...and we all got different answers for a question...and nobody knows who is right now lol

Answer 3

the question was y' = (5x +2y)/x

Answer 4

Let's start by multiplying both sides by \(x\): \(xy'-2y=5x\). This is a famous form of differential equations called Cauchy-Euler equation. To find the solution of the associated homogenous equation, assume a solution of the form \(y_c=x^m \implies x(mx^{m-1})-2x^m=0\implies x^m(m-2)=0 \). That gives the solution \(m=2\), which yield to the solution \(y_c=c_1x^2\). I'll find the particular solution in another post.

Answer 5

It's very easy to find the particular solution for this problem by assuming a solution of the form \(y_p=Ax\), where A is a real number to be found. Plug that on the original equation and solve for A: \(Ax-2Ax=5x \implies -Ax=5x \implies A=-5\). So, the particular solution \(y_p=-5x\) and the general solution would be then \(y=cx^2-5x.\)

Answer 6

I hope you're the one who got it right! :D

Answer 7

if the general solution is x^2-5x + c.....no i didn't get it right...and neither did anyone else for that matter lol

Answer 8

Lol, It's \(y=cx^2-5x\).