Method of Undetermined Coefficients

For the equation $\displaystyle y''+4y=t^2+3e^t$: I have split up the particular solution into two parts, so that I have

$\displaystyle Y_p=At^2+Bt+C=t^2$ and $\displaystyle Y_{p2}=Ae^t=3e^t$

which gives me

$\displaystyle Y_p=\frac{1}{4}t^2$ and $\displaystyle Y_{p2}=\frac{1}{5}e^t$

The solution of the corresponding homogeneous equation is of course $\displaystyle y=c_1cos(2t)+c_2sin(2t)$. So for my answer I get $\displaystyle \frac{1}{4}t^2+\frac{1}{5}e^t+\frac{1}{5}cos(2t)+\ frac{9}{10}sin(2t)$

Where did I go wrong?