How can I get mathematica to solve the non-homogeneous differential equation with undetermined coefficients listed below?
Solve $\ y''(t)+3y'(t) = 2t^4 $, using: $\ y_p(t) = t(A_0t^4+A_1t^3+A_2t^2+A_3t+A_4) $
where $\ y_p(t) $ is a particular solution
incidentally, $\ y'(t) = A_4 + 2 A_3 t + 3 A_2 t^2 + 4 A_1 t^3 + 5 A_0 t^4 $ and $\ y''(t) = 2 A_3 + 6 A_2 t + 12 A_1 t^2 + 20 A_0 t^3 $
I'd like a solution that doesn't use
DSolve because I can already solve the entire differential equation with that. I just need to see this particular part for verification of my work. Any suggestions?