\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \cot \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.072509 (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 = 0.858 (sec), leaf count = 85 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{\tan \left ( x \right ) }\sqrt {1- \left ( \left ( \tan \left ( x \right ) \right ) ^{2} +1 \right ) ^{-1}}\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1} \left ( 1+{\frac {1}{\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2 }+1}}} \right ) ^{-1}},y \left ( x \right ) ={\frac {{\it \_C1}}{\tan \left ( x \right ) } \left ( 1+{\frac {1}{\sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1}}} \right ) \sqrt { \left ( \tan \left ( x \right ) \right ) ^{2}+1}{\frac {1}{\sqrt {1- \left ( \left ( \tan \left ( x \right ) \right ) ^{2}+1 \right ) ^{-1}}}}} \right \} \]