ODE
\[ y'(x)=\sin (x) (\csc (y(x))-\cot (y(x))) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.370059 (sec), leaf count = 21
\[\left \{\left \{y(x)\to 2 \sin ^{-1}\left (e^{\frac {1}{4} (-2 \cos (x)+c_1)}\right )\right \}\right \}\]
Maple ✓
cpu = 0.093 (sec), leaf count = 14
\[[y \left (x \right ) = \arccos \left ({\mathrm e}^{-\cos \left (x \right )} \textit {\_C1} +1\right )]\] 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))
Maple raw output
[y(x) = arccos(exp(-cos(x))*_C1+1)]