\[ y'(x) \cos (y(x)) (\cos (y(x))-\sin (\alpha ) \sin (x))+\cos (x) (\cos (x)-\sin (\alpha ) \sin (y(x)))=0 \] ✓ Mathematica : cpu = 0.165351 (sec), leaf count = 32
\[\text {Solve}\left [c_1+2 y(x)+\sin (2 y(x))+2 x+\sin (2 x)=4 \sin (\alpha ) \sin (x) \sin (y(x)),y(x)\right ]\]
✓ Maple : cpu = 0.302 (sec), leaf count = 33
\[ \left \{ {\frac { \left ( -2\,\sin \left ( \alpha \right ) \sin \left ( x \right ) +\cos \left ( y \left ( x \right ) \right ) \right ) \sin \left ( y \left ( x \right ) \right ) }{2}}+{\frac {\cos \left ( x \right ) \sin \left ( x \right ) }{2}}+{\frac {x}{2}}+{\it \_C1}+{\frac {y \left ( x \right ) }{2}}=0 \right \} \]