2.6.10.8 ✓ Sympy. Time used: 3.115 (sec). Leaf size: 24

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

\begin{gather*} \begin {aligned} y{\left (x \right )} = C_{1} e^{- \frac {4 x^{\frac {3}{2}}}{3} - \frac {\cos {\left (x^{2} - 1 \right )}}{2}} \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')