2.6.6.8 ✓ Sympy. Time used: 0.313 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
n = Function("n") 
ode = Eq(-x*(n(x)**2 + 1) + Derivative(n(x), x),0) 
ics = {} 
dsolve(ode,func=n(x),ics=ics)
 

\begin{gather*} \begin {aligned} n{\left (x \right )} = \tan {\left (C_{1} + \frac {x^{2}}{2} \right )} \end {aligned} \end{gather*}

Python version: 3.12.3 (main, Aug 14 2025, 17:47:21) [GCC 13.3.0] 
Sympy version 1.14.0
 

classify_ode(ode,func=n(x)) 
 
('separable', '1st_exact', '1st_rational_riccati', '1st_power_series', 'lie_group', 'separable_Integral', '1st_exact_Integral')