2.2.3.7 ✓ Sympy. Time used: 0.376 (sec). Leaf size: 12

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

\begin{gather*} \begin {aligned} y{\left (x \right )} = \frac {C_{1} x}{x + \frac {1}{b}} + b \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=y(x)) 
 
('factorable', 'separable', '1st_exact', '1st_linear', 'Bernoulli', 'almost_linear', 'lie_group', 'separable_Integral', '1st_exact_Integral', '1st_linear_Integral', 'Bernoulli_Integral', 'almost_linear_Integral')