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## Homework Statement

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

**2. The attempt at a solution**

d/dx (y) = d/dx (Ax^2+Bx+C) = 2Ax+B

y' = 2Ax+B

d/dx (y') = d/dx (2Ax+B) = 2A

y'' = 2A

Now subbing back into the differential equation given:

(2A) + (2Ax+B) - 2y = x^2

2A + (2Ax+B) - 2(Ax^2+Bx+C) = x^2

2A + 2Ax + B - 2Ax^2 - 2Bx - 2C = x^2

Moving the left hand side around:

(2A-2C+B) + (2A-2B)x - 2Ax^2 = x^2

However, now I have to solve for the constants and I'm not exactly sure how to figure that out. Any help would be great! Thanks guys :D

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