3 Mathematica. Time used: 2.589 (sec). Leaf size: 39

ode=D[v[u],u]+u^2*v[u]==Sin[u]; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]

\begin{align*} v(u)&\to e^{-\frac {u^3}{3}} \left (\int _1^ue^{\frac {K[1]^3}{3}} \sin (K[1])dK[1]+c_1\right ) \end{align*}