ODE
\[ y'(x)+\sin (2 x) \csc (2 y(x))=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.368501 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\frac {1}{2} \cos ^{-1}(-\cos (2 x)-2 c_1)\right \},\left \{y(x)\to \frac {1}{2} \cos ^{-1}(-\cos (2 x)-2 c_1)\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {\arccos \left (-\cos \left (2 x \right )+4 \textit {\_C1} \right )}{2}\right ]\] Mathematica raw input
DSolve[Csc[2*y[x]]*Sin[2*x] + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*ArcCos[-2*C[1] - Cos[2*x]]}, {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))
Maple raw output
[y(x) = 1/2*arccos(-cos(2*x)+4*_C1)]