Solving Derivative Problem: Find Constants A, B & C

[temaire]

Homework Statement

Find the constants A, B, and C such that the function y=Ax^{2}+Bx+C satisfies the differential equation y^{''}+y^{'}-2y=x^{2}.

The Attempt at a Solution

I know that y^{''}+y^{'}-2Ax^{2}-2Bx-2C=x^{2} and that y^{'}=2Ax+B and y^{''}=2A, but I'm really stuck at this point. Any help would be appreciated.

 

[lanedance]

almost there, substitute in for y & y'

each power of x will give you an equation that must be solved for the solution to satisfy teh differential equation

eg. the co-efficients of x^1 must add up to zero