2.4.6.5 ✓ Sympy. Time used: 0.707 (sec). Leaf size: 14

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

\begin{gather*} \begin {aligned} y{\left (x \right )} = C_{1} e^{- \sin {\left (x \right )}} + \sin {\left (x \right )} - 1 \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', '1st_exact', '1st_linear', 'Bernoulli', 'almost_linear', '1st_power_series', 'lie_group', '1st_exact_Integral', '1st_linear_Integral', 'Bernoulli_Integral', 'almost_linear_Integral')