\[ y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.0847473 (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 = 0.351 (sec), leaf count = 77
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{\tan \left ( x \right ) } \left ( 1+\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1} \right ) {\frac {1}{\sqrt {{\frac { \left ( \tan \left ( x \right ) \right ) ^{2}}{ \left ( \tan \left ( x \right ) \right ) ^{2}+1}}}}}},y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( \left ( \tan \left ( x \right ) \right ) ^{2}+1 \right ) }{\tan \left ( x \right ) }\sqrt {{\frac { \left ( \tan \left ( x \right ) \right ) ^{2}}{ \left ( \tan \left ( x \right ) \right ) ^{2}+1}}} \left ( 1+\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1} \right ) ^{-1}} \right \} \]