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 the differential equation

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