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## Homework Statement

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

## The Attempt at a Solution

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