\[ y'(x) \cos (y(x)) (\cos (y(x))-\sin (\alpha ) \sin (x))+\cos (x) (\cos (x)-\sin (\alpha ) \sin (y(x)))=0 \] ✓ Mathematica : cpu = 0.520555 (sec), leaf count = 43
\[\text {Solve}\left [4 \sin (\alpha ) \sin (x) \sin (y(x))-4 \left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right )-2 x-\sin (2 x)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.345 (sec), leaf count = 33
\[ \left \{ {\frac { \left ( -2\,\sin \left ( \alpha \right ) \sin \left ( x \right ) +\cos \left ( y \left ( x \right ) \right ) \right ) \sin \left ( y \left ( x \right ) \right ) }{2}}+{\frac {\cos \left ( x \right ) \sin \left ( x \right ) }{2}}+{\frac {x}{2}}+{\it \_C1}+{\frac {y \left ( x \right ) }{2}}=0 \right \} \]