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