# Thread: ODE proof type question

1. ## ODE proof type question

Hi, I am struggling with the following question:

if yp1 satisfies y''p1 + p(x)y'p1 + q(x)yp1 = r1(x), yp2 satisfies y''p2 + p(x)y'p2 + q(x)yp2 = r2(x) and yh satisfies y''h + p(x)y'h + q(x)yh = 0 , show that y = yh+ yp1 + yp2 satisfies y'' + p(x)y' + q(x)y = r1(x) + r2(x)

Usually I would post my attempt at a question on here but I actually don't know how to get started on this one. I am doing okay actually using this principle to solve ODEs so far, but I don't know how to prove it.

Thanks for any help, and I hope the above is readable.

Andy

2. ## Re: ODE proof type question

Hey andy000.

Hint: Try taking your solution, getting its first and second derivatives and then plugging into the differential equation and showing that it holds.