\[ \boxed { \left ( a \left ( \sin \left ( x \right ) \right ) ^{2}+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) \sin \left ( 2\,x \right ) +Ax \left ( a \left ( \sin \left ( x \right ) \right ) ^{2}+c \right ) =0} \]
Mathematica: cpu = 0.050506 (sec), leaf count = 77 \[ \left \{\left \{y(x)\to \frac {\frac {1}{2} a A x^2-\frac {1}{2} a A x \sin (2 x)-\frac {1}{4} a A \cos (2 x)+A c x^2}{a \cos (2 x)-a-2 b}+\frac {c_1}{a \cos (2 x)-a-2 b}\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 56 \[ \left \{ y \left ( x \right ) ={\frac {-2\,A\sin \left ( 2\,x \right ) ax+ 2\,Aa{x}^{2}+4\,Ac{x}^{2}-A\cos \left ( 2\,x \right ) a-8\,{\it \_C1}}{4 \,a\cos \left ( 2\,x \right ) -4\,a-8\,b}} \right \} \]