Solve differential equations containing $x''$ Solve the equation $$x'' + 3x' = 20e^{2t}$$ if $x(0) = 0$ and $x'(0) = 1$. 

I am pretty sure $x$ must contain $e^{2t}$, but other than that, I'm not really sure how to proceed from here. Any help would really be appreciated!
Hints: Put $y=x'$. The homogeneous  equation becomes $y'+3y=0$ whose solution is $y=ae^{-3t}$. Integrate to get $x$. A particular solution of the type $ce^{2t}$ exists. Add the particular solution to the general solution of the homogeneous  equation and the apply the intial conditions. 

Answer: $e^{-3t}-3+2e^{2t}$.
For your work: The solution is given by $$x(t)=-\frac{1}{3} c_1 e^{-3 t}+c_2+2 e^{2 t}$$