2.1.21.5 ✓ Sympy. Time used: 2.644 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-x(t)*tan(t) - 4*sin(t) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\begin{gather*} \begin {aligned} x{\left (t \right )} = \frac {C_{1}}{\cos {\left (t \right )}} - 2 \cos {\left (t \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=x(t)) 
 
('1st_exact', '1st_linear', 'Bernoulli', 'almost_linear', '1st_power_series', 'lie_group', '1st_exact_Integral', '1st_linear_Integral', 'Bernoulli_Integral', 'almost_linear_Integral')