y'''-3y''+3y'-y=x-4e^x
ok so i found the roots of the equation where m = 1 and then i got my yc equation which was also pretty straight forward.
what i am having problems with is the yp equation,
i made my guess to be: Ax + Bx^3e^x <--- my book said i was wrong?
any help would be appreciated...
When you plug that into the LHS, the operator will annihilate the exponential, so there's no way you'll get the RHS out of that. Because the root m = 1 has multiplicity 3, your particular solution will have to look something like slapmaxwell1's candidate. I might recommend have something more like
That might be overkill, but it might not. A hunch: any of those constant that are superfluous will be easy to solve for, I think. So I don't think you'll waste too much time doing it this way.