Homework Help: Derivative Problem

1. Nov 1, 2009

temaire

1. The problem statement, all variables and given/known data
Find the constants A, B, and C such that the function $$y=Ax^{2}+Bx+C$$ satisfies the differential equation $$y^{''}+y^{'}-2y=x^{2}$$.

3. 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.

2. Nov 2, 2009

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