ODE
\[ x^4 y'(x)+x^3 y(x)+\csc (x y(x))=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
Book solution method
Change of Variable, new dependent variable
Mathematica ✓
cpu = 1.38409 (sec), leaf count = 40
\[\left \{\left \{y(x)\to -\frac {\cos ^{-1}\left (-\frac {1}{2 x^2}+c_1\right )}{x}\right \},\left \{y(x)\to \frac {\cos ^{-1}\left (-\frac {1}{2 x^2}+c_1\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.494 (sec), leaf count = 26
\[\left [y \left (x \right ) = \frac {\pi -\arccos \left (\frac {2 x^{2} \textit {\_C1} +1}{2 x^{2}}\right )}{x}\right ]\] 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*1/x^2 + C[1]]/x)}, {y[x] -> ArcCos[-1/2*1/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))
Maple raw output
[y(x) = (Pi-arccos(1/2*(2*_C1*x^2+1)/x^2))/x]