2.3.4.4 ✓ Sympy. Time used: 2.198 (sec). Leaf size: 26

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

\begin{gather*} \begin {aligned} \left [ y{\left (x \right )} = \pi - \frac {\operatorname {acos}{\left (C_{1} - \cos {\left (2 x \right )} \right )}}{2}, \ y{\left (x \right )} = \frac {\operatorname {acos}{\left (C_{1} - \cos {\left (2 x \right )} \right )}}{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=y(x)) 
 
('factorable', 'separable', '1st_power_series', 'lie_group', 'separable_Integral')