What is the solution to a nonhomogenous second order differential equation?

[jesuslovesu]

[SOLVED] Nonhomogenous Second Order DE

Homework Statement

y'' - 2y' - 3y = -3te^{-t}
Solve

Homework Equations

The Attempt at a Solution

Well first I tried
Y(t) = Ate^{-t}
then
Y(t) = At^2e^{-t}
then
Y(t) = At^3e^{-t}
and
Y(t) = At^3e^{-t} + Bt^2e^{-t}
but I can't seem to get the correct form.

Does anyone know what form I need my Y(t) in order to solve this?

 

[jesuslovesu]

I believe I end up with a term like
Ae^{-t} = -3te^{-t} which I don't believe I can do anything with?

In fact, in all the cases I've tried I always seem to get something like Ae^{-t} which never cancels out so I can never equation -3te^{-t} to any of my terms

 

[jesuslovesu]

ah finally got it with At^2e^{-1}+Bte^{-1}
bah that sucked