3 Mathematica. Time used: 0.613 (sec). Leaf size: 41

ode=Sec[x]^2*Tan[y[x]]*D[y[x],x]+Sec[y[x]]^2*Tan[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]

\begin{align*} y(x)&\to -\frac {1}{2} \arccos (-\cos (2 x)-2 c_1)\\ y(x)&\to \frac {1}{2} \arccos (-\cos (2 x)-2 c_1) \end{align*}