2.6.12.6 ✓ Mathematica. Time used: 0.051 (sec). Leaf size: 22

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

\begin{align*} v(u)&\to 1+c_1 e^{-u^2}\\ v(u)&\to 1 \end{align*}