y''(x) +3(y'(x))+2y=4e^(2x)+7

this is my ODE, it is inhomogeneous linear and second order with constant coefficients.

have i got this correct in saying the general solution is:

y=(1/3)*e^(2x)+7/2 ???

please could someone verify this quickly for me? im just curious as to whether or not i should be adding some unknown constants or other terms as well?

thanks (Headbang)