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 = 1.51103 (sec), leaf count = 40
\[\left \{\left \{y(x)\to -\frac {\cos ^{-1}\left (c_1-\frac {1}{2 x^2}\right )}{x}\right \},\left \{y(x)\to \frac {\cos ^{-1}\left (c_1-\frac {1}{2 x^2}\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.405 (sec), leaf count = 23
\[ \left \{ -{\it \_C1}+{\frac {-2\,\cos \left ( xy \left ( x \right ) \right ) {x}^{2}-1}{{x}^{2}}}=0 \right \} \] 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*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