Find the general solution of the second-order inhomogeneous differential equation

y''+3y'+2y=$\displaystyle e^{2x}cos(x)$

So far I have:

$\displaystyle y(x)=Ae^{2x}sin(3x) +Be^{2x}cos(3x)$

$\displaystyle \frac{dy}{dx}= \frac{1}{5}(e^{2x}cos(x) +3e^{2x} sin(x))$

$\displaystyle \frac{d^{2}y}{dx^{2}}= \frac{1}{25}(-e^{2x}cos(x) +7e^{2x} sin(x))$

After this I substituted $\displaystyle \frac{dy}{dx} and \frac{d^{2}y}{dx^{2}}$ in to the origional equation. I'm not sure if what im doing is correct. And after this step I have no Idea what to do. Please Help, Thanks