confused on how i'm suppose to prove this DE principal, suppose.. .:Resolved:.

[voidflux]

Hello everyone,


I have some notes on the principal of superpostion of solutions for homogenous equations. It sounds comlex but it really isn't. I know how to solve prolems like this but our professor comes out of the blew and says, prove the principal.

Well it says

y'' + p(x)y' + q(x)y = 0; <----equation 1
If y1 and y2 are two solutions of the above equation(1), then
y = c1y1 + c2y2; //where c1 and c2 are constants
is also a solution. And i'm suppose to prove that y = c1y1 + c2y2 is also a solution. She said its really simple. She said all we have to do is take the first derivative and 2nd derivative of y = c1y1+c2y2 and then plug that value into the above equation (1). But this confused because if i take the first derivative of y, i would get:

y' = c1 + c2;
y'' = 0 + 0;

what am i supose to do with that mess? after plugging it into the above equation i get no where. Any idea's on how i am suppoe to prove this?

Thanks!!