\[ y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.0921654 (sec), leaf count = 31
\[\left \{\left \{y(x)\to c_1 \csc ^2\left (\frac {x}{2}\right )\right \},\left \{y(x)\to c_1 \sec ^2\left (\frac {x}{2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.213 (sec), leaf count = 77
\[y \relax (x ) = \frac {c_{1} \left (1+\tan ^{2}\relax (x )\right ) \sqrt {\frac {\tan ^{2}\relax (x )}{1+\tan ^{2}\relax (x )}}}{\left (1+\sqrt {1+\tan ^{2}\relax (x )}\right ) \tan \relax (x )}\]