2.5.1.5 Sympy
from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x)**2 - y(x) + 2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 
NotImplementedError : The given ODE Derivative(y(x), x) - (sqrt(x*y(x) + 1) - 1)/x cannot be solved
 
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=y(x)) 
 
('factorable', 'lie_group')