2.6.8.4 ✓ Sympy. Time used: 0.453 (sec). Leaf size: 15

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

\begin{gather*} \begin {aligned} v{\left (u \right )} = \sin {\left (C_{1} - 2 \sqrt {1 - u^{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=v(u)) 
 
('factorable', 'separable', '1st_power_series', 'lie_group', 'separable_Integral')