1. The problem statement, all variables and given/known data Given that y=x^2 is a solution to the differential equation: (x^2)y'' + 2xy' - 6y = 0 <--- Eq.(1) find the general solution of the differential equation (x^2)y'' + 2xy' - 6y = 10(x^7) + 15(x^2) <--- Eq.(2) Hence write down a second linear dependent solution of equation (1) and a particular solution of equation (2). 2. Relevant equations I've basically concluded that variation of parameters is necessary. I don't think I completely understand what is being asked. 3. The attempt at a solution I tried letting y= V(y1) = V(X^2) hence y'= (x^2)V' + 2xV and y''= (x^2)V'' + 2xV' + 2V Here is where I think I'm getting confused, sub. back in to (1) I get: V''(x^4)+2(x^3)V'+2V(x^2)+2(x^3)V'+4(x^2)V-6V(x^2)=0 which equals V''(x^4)+4(x^3)V"=0 This is where I come to a dead end, any help or advice would be greatly appreciated, thank you.