2.1.10.7 ✓ Sympy. Time used: 0.621 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-sqrt(x(t)**2 - 1) + Derivative(x(t), t),0) 
ics = {x(0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\begin{gather*} \begin {aligned} x{\left (t \right )} = \cosh {\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)) 
 
('separable', '1st_exact', '1st_power_series', 'lie_group', 'separable_Integral', '1st_exact_Integral')