ODE
\[ y'(x)+\sin (2 x) \csc (2 y(x))=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0273169 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\frac {1}{2} \cos ^{-1}\left (-2 c_1-\cos (2 x)\right )\right \},\left \{y(x)\to \frac {1}{2} \cos ^{-1}\left (-2 c_1-\cos (2 x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 14
\[ \left \{ {\it \_C1}+\cos \left ( 2\,x \right ) +\cos \left ( 2\,y \left ( x \right ) \right ) =0 \right \} \] Mathematica raw input
DSolve[Csc[2*y[x]]*Sin[2*x] + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -ArcCos[-2*C[1] - Cos[2*x]]/2}, {y[x] -> ArcCos[-2*C[1] - Cos[2*x]]/2}}
Maple raw input
dsolve(diff(y(x),x)+sin(2*x)*csc(2*y(x)) = 0, y(x),'implicit')
Maple raw output
_C1+cos(2*x)+cos(2*y(x)) = 0