2.7.8.4 ✓ Mathematica. Time used: 0.636 (sec). Leaf size: 42

ode=D[y[x],{x,2}]+3*y[x]==Sin[x]+1/3*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sin (x)}{2}-\frac {1}{18} \sin (3 x)+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \end{align*}