2.3.3.5 ✓ Mathematica. Time used: 1.277 (sec). Leaf size: 62

ode=D[x[t],{t,2}]+2*D[x[t],t]+4*x[t]==Exp[t]*Cos[2*t]; 
ic={x[0]==0,Derivative[1][x][0] == 1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{73} e^{-t} \left (8 e^{2 t} \sin (2 t)+17 \sqrt {3} \sin \left (\sqrt {3} t\right )+3 e^{2 t} \cos (2 t)-3 \cos \left (\sqrt {3} t\right )\right ) \end{align*}