ODE
\[ y'(x)=\sin (x) (\csc (y(x))-\cot (y(x))) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.112868 (sec), leaf count = 21
\[\left \{\left \{y(x)\to 2 \sin ^{-1}\left (e^{\frac {1}{4} \left (c_1-2 \cos (x)\right )}\right )\right \}\right \}\]
Maple ✓
cpu = 0.042 (sec), leaf count = 15
\[ \left \{ {\it \_C1}+\cos \left ( x \right ) +\ln \left ( 1-\cos \left ( y \left ( x \right ) \right ) \right ) =0 \right \} \] Mathematica raw input
DSolve[y'[x] == (-Cot[y[x]] + Csc[y[x]])*Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> 2*ArcSin[E^((C[1] - 2*Cos[x])/4)]}}
Maple raw input
dsolve(diff(y(x),x) = sin(x)*(csc(y(x))-cot(y(x))), y(x),'implicit')
Maple raw output
_C1+cos(x)+ln(1-cos(y(x))) = 0