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## Homework Statement

Find the appropiate particular solution form for

y''' - y'' - 12y' = x - 2x*e^-(3x)

DO NOT SOLVE FOR THE COEFFICIENTS

## Homework Equations

Just guessing proper solution forms for nonhomogeneous second order D.Es with undetermined coefficients.

## The Attempt at a Solution

Ok, as far as I know the solution in my mind was...

Ax + B + (Cx^2 + Dx) e ^(-3x)

The homogeneous solution was yc = c1 + c2e^(4x) + c3e^(-3x)

BUT

the solution is Ax + Bx^2 + (Cx + Dx^2)e^(-3x)

I don;t know why the B has x^2, and I don't know why D and C are switched around. I've been going at this for a good hour.

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