2.6.2.4 ✓ Mathematica. Time used: 0.012 (sec). Leaf size: 15

ode=Sec[theta]^2==m/k*D[s[theta],theta]; 
ic={}; 
DSolve[{ode,ic},s[theta],theta,IncludeSingularSolutions->True]
 

\begin{align*} s(\theta )&\to \frac {k \tan (\theta )}{m}+c_1 \end{align*}