\[ y'(x) \cos (y(x)) (\cos (y(x))-\sin (\alpha ) \sin (x))+\cos (x) (\cos (x)-\sin (\alpha ) \sin (y(x)))=0 \] ✓ Mathematica : cpu = 0.55124 (sec), leaf count = 43
DSolve[Cos[x]*(Cos[x] - Sin[alpha]*Sin[y[x]]) + Cos[y[x]]*(Cos[y[x]] - Sin[alpha]*Sin[x])*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [4 \sin (\alpha ) \sin (x) \sin (y(x))-4 \left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right )-2 x-\sin (2 x)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.521 (sec), leaf count = 33
dsolve(diff(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-sin(alpha)*sin(y(x)))*cos(x) = 0,y(x))
\[\frac {\left (-2 \sin \left (\alpha \right ) \sin \left (x \right )+\cos \left (y \left (x \right )\right )\right ) \sin \left (y \left (x \right )\right )}{2}+\frac {\sin \left (x \right ) \cos \left (x \right )}{2}+\frac {x}{2}+c_{1}+\frac {y \left (x \right )}{2} = 0\]