2.1.6.6 ✓ Sympy. Time used: 0.209 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) - cos(t)/sin(t),0) 
ics = {x(1): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\begin{gather*} \begin {aligned} x{\left (t \right )} = \log {\left (\sin {\left (t \right )} \right )} - \log {\left (\sin {\left (1 \right )} \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)) 
 
('factorable', 'nth_algebraic', 'separable', '1st_exact', '1st_linear', 'Bernoulli', 'lie_group', 'nth_linear_constant_coeff_variation_of_parameters', 'nth_linear_euler_eq_nonhomogeneous_variation_of_parameters', 'nth_algebraic_Integral', 'separable_Integral', '1st_exact_Integral', '1st_linear_Integral', 'Bernoulli_Integral', 'nth_linear_constant_coeff_variation_of_parameters_Integral', 'nth_linear_euler_eq_nonhomogeneous_variation_of_parameters_Integral')