2.6.6.7 ✓ Mathematica. Time used: 0.217 (sec). Leaf size: 30

ode=D[n[x],x]==(n[x]^2+1)*x; 
ic={}; 
DSolve[{ode,ic},n[x],x,IncludeSingularSolutions->True]
 

\begin{align*} n(x)&\to \tan \left (\frac {x^2}{2}+c_1\right )\\ n(x)&\to -i\\ n(x)&\to i \end{align*}