Differential Equation

[Idealistic]

The equation: y'' + y' - 2y = x^2. Find constants A, B, and C such that the function y = Ax^2 + Bx^2 + C satisfies this equation. I know that the original fucniton is quadratic from description in the question, but im not exactly sure of what to do. Am I supposed to rearrange the equation with respect to y, and then do a bunch of substitution? I'm really not sure.

 

[galactus]

Find the first and second derivatives of your quadratic.

\(\displaystyle y'=2Ax+B\)

\(\displaystyle y''=2A\)

Sub them into your DE and equate coefficients to solve for A, B, and C.

Once you have A, B, and C you can sub them back in and see if it reduces to x^2. If you do it right, it will.