4.8.24 $x^4{y}^{\prime }(x)+x^{3}y(x)+\csc (xy(x))=0$

ODE
$$x^4{y}^{\prime }(x)+x^{3}y(x)+\csc (xy(x))=0$$ ODE Classification

[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

Book solution method
Change of Variable, new dependent variable

Mathematica ✓
cpu = 1.51103 (sec), leaf count = 40

$$\{\{y(x)\to -\frac{{\cos }^{-1}(c_1-\frac{1}{2x^2})}{x}\},\{y(x)\to \frac{{\cos }^{-1}(c_1-\frac{1}{2x^2})}{x}\}\}$$

Maple ✓
cpu = 0.405 (sec), leaf count = 23

$$\{-\mathit{\_}\mathit{C}\mathit{1}+\frac{-2\cos \left(xy\left(x\right)\right)x^2-1}{x^2}=0\}$$ Mathematica raw input

DSolve[Csc[x*y[x]] + x^3*y[x] + x^4*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(ArcCos[-1/(2*x^2) + C[1]]/x)}, {y[x] -> ArcCos[-1/(2*x^2) + C[1]]/x}
}

Maple raw input

dsolve(x^4*diff(y(x),x)+x^3*y(x)+csc(x*y(x)) = 0, y(x),'implicit')

Maple raw output

-_C1+(-2*cos(x*y(x))*x^2-1)/x^2 = 0