\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) \sin \left ( 2\,x \right ) -\cos \left ( 2\,x \right ) =0} \]
Mathematica: cpu = 241.061111 (sec), leaf count = 31 \[ \text {DSolve}\left [y'(x)-y(x)^2-y(x) \sin (2 x)-\cos (2 x)=0,y(x),x\right ] \]
Maple: cpu = 0.468 (sec), leaf count = 198 \[ \left \{ y \left ( x \right ) = \left ( 2\,{\frac {{\it \_C1}\,\cos \left ( 2\,x \right ) }{\sqrt {2\,\cos \left ( 2\,x \right ) +2}}{\it HeunCPrime} \left ( 1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) \left ( {\it \_C1}\,{\it HeunC} \left ( 1,1/2,-1/ 2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) \sqrt { 2\,\cos \left ( 2\,x \right ) +2}+{\it HeunC} \left ( 1,-1/2,-1/2,-1,{ \frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) \right ) ^{-1 }}+{1 \left ( 2\,{\it HeunCPrime} \left ( 1,1/2,-1/2,-1,{\frac {7}{8}},1 /2\,\cos \left ( 2\,x \right ) +1/2 \right ) {\it \_C1}+{\it HeunCPrime} \left ( 1,-{\frac {1}{2}},-{\frac {1}{2}},-1,{\frac {7}{8}},{\frac { \cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}} \right ) \sqrt {2\,\cos \left ( 2\,x \right ) +2}+2\,{\it HeunC} \left ( 1,1/2,-1/2,-1,{\frac {7 }{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) {\it \_C1} \right ) { \frac {1}{\sqrt {2\,\cos \left ( 2\,x \right ) +2}}} \left ( {\it \_C1}\, {\it HeunC} \left ( 1,{\frac {1}{2}},-{\frac {1}{2}},-1,{\frac {7}{8}}, {\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}} \right ) \sqrt {2 \,\cos \left ( 2\,x \right ) +2}+{\it HeunC} \left ( 1,-{\frac {1}{2}},-{ \frac {1}{2}},-1,{\frac {7}{8}},{\frac {\cos \left ( 2\,x \right ) }{2}} +{\frac {1}{2}} \right ) \right ) ^{-1}} \right ) \sin \left ( 2\,x \right ) \right \} \]
Sage: cpu = 0.06 (sec), leaf count = 0 \[ \left [\left [\left [y\left (x\right ) = 0, u \cos \left (2 \, x\right ) = 0\right ]\right ], \text {\texttt {riccati}}\right ] \]