2.1.15.8 ✓ Sympy. Time used: 1.512 (sec). Leaf size: 24

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

\begin{gather*} \begin {aligned} x{\left (t \right )} = C_{1} e^{- \int \limits ^{\frac {t}{x{\left (t \right )}}} \frac {\cos {\left (\frac {1}{u_{1}} \right )}}{u_{1} \cos {\left (\frac {1}{u_{1}} \right )} - 1}\, du_{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=x(t)) 
 
('1st_homogeneous_coeff_best', '1st_homogeneous_coeff_subs_indep_div_dep', '1st_homogeneous_coeff_subs_dep_div_indep', 'lie_group', '1st_homogeneous_coeff_subs_indep_div_dep_Integral', '1st_homogeneous_coeff_subs_dep_div_indep_Integral')