2.3.4.5 ✓ Mathematica. Time used: 1.948 (sec). Leaf size: 67

ode=D[x[t],{t,2}]-D[x[t],t]+x[t]==Sin[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}{39} \left (-9 \sin (2 t)+40 \sqrt {3} e^{t/2} \sin \left (\frac {\sqrt {3} t}{2}\right )+6 \cos (2 t)-6 e^{t/2} \cos \left (\frac {\sqrt {3} t}{2}\right )\right ) \end{align*}