$\displaystyle y"+9y = t^2(e^{3t}) + 6$

ok wow, I have racked my brain at on this for about 5 hours with and without a study group.

I cannot seem how to set up the initial part of finding the particular solution.

I had found one variable and one point which was c = 1/162 but couldnt find A, or B.

I tried using $\displaystyle y(t)=(e^{3t})(at^{2} + bt +c)$ but got stock when plugging in the second derivative in and couldnt not find answer for the rest of the coefficients.

what am I doing wrong?