\[ y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.0314301 (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 = 0.119 (sec), leaf count = 85
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{\tan \left ( x \right ) }\sqrt {1- \left ( \left ( \tan \left ( x \right ) \right ) ^{2}+1 \right ) ^{-1}}\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1} \left ( {\frac {1}{\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1}}}+1 \right ) ^{-1}},y \left ( x \right ) ={\frac {{\it \_C1}}{\tan \left ( x \right ) } \left ( {\frac {1}{\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1}}}+1 \right ) \sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1}{\frac {1}{\sqrt {1- \left ( \left ( \tan \left ( x \right ) \right ) ^{2}+1 \right ) ^{-1}}}}} \right \} \]