\[ y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.104328 (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 = 0.175 (sec), leaf count = 77
\[\left \{y \left (x \right ) = \frac {c_{1} \left (1+\sqrt {\tan ^{2}\left (x \right )+1}\right )}{\sqrt {\frac {\tan ^{2}\left (x \right )}{\tan ^{2}\left (x \right )+1}}\, \tan \left (x \right )}, y \left (x \right ) = \frac {c_{1} \left (\tan ^{2}\left (x \right )+1\right ) \sqrt {\frac {\tan ^{2}\left (x \right )}{\tan ^{2}\left (x \right )+1}}}{\left (1+\sqrt {\tan ^{2}\left (x \right )+1}\right ) \tan \left (x \right )}\right \}\]