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

Here is what I have done so far:

$\displaystyle y' = 2Ax + B$

$\displaystyle y'' = 2A$

$\displaystyle 2A + 2Ax + B - 2y = x^2$

$\displaystyle 2A(1 + x) = x^2 + 2y - B$

But now I don't know where to go next. Can anybody help, please? Thanks.