2.4.6.4 ✓ Mathematica. Time used: 0.053 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to \sin (x)+c_1 e^{-\sin (x)}-1 \end{align*}