Find the appropiate particular solution form for
y''' - y'' - 12y' = x - 2x*e^-(3x)
DO NOT SOLVE FOR THE COEFFICIENTS
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)
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.