3 Mathematica. Time used: 1.585 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to \arctan (-\sec (x)+c_1)\\ y(x)&\to -\frac {\pi }{2}\\ y(x)&\to \frac {\pi }{2} \end{align*}