I'm supposed to find the solution this initial value problem using the method of undetermined coefficients

$\displaystyle

y'' - 2y' - 3y = 3te^{2t}, y(0)=1, y'(0)=0.$

My guess was to use $\displaystyle Y(t) = Ate^{2t} + Be^{2t}$ for the particular solution, but this led me to the wrong answer.

I have a hunch that I should use $\displaystyle Y(t) = t(Ate^{2t} + Be^{2t})$ but I have no idea why, since $\displaystyle e^{2t}$ is not part of the complimentary solution.

I appreciate any help.