\[ \boxed { y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \left ( \sin \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2}\cos \left ( x \right ) \sin \left ( x \right ) -1=0} \]
Mathematica: cpu = 0.033004 (sec), leaf count = 36 \[ \left \{\left \{y(x)\to -\sqrt {c_1+2 x} \csc (x)\right \},\left \{y(x)\to \sqrt {c_1+2 x} \csc (x)\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {1}{\sin \left ( x \right ) }\sqrt { 2\,x+{\it \_C1}}},y \left ( x \right ) =-{\frac {1}{\sin \left ( x \right ) }\sqrt {2\,x+{\it \_C1}}} \right \} \]