4.3.19 $y^{\prime }(x)=\sin (x)(\csc (y(x))-\cot (y(x)))$

ODE
$$y^{\prime }(x)=\sin (x)(\csc (y(x))-\cot (y(x)))$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.112868 (sec), leaf count = 21

$$\left\{\{y(x)\to 2{\sin }^{-1}\left(e^{\frac{1}{4}(c_1-2\cos (x))}\right)\}\right\}$$

Maple ✓
cpu = 0.042 (sec), leaf count = 15

$$\{\mathit{\_}\mathit{C}\mathit{1}+\cos \left(x\right)+\ln (1-\cos \left(y\left(x\right)\right))=0\}$$ 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