##### 4.19.39 $$x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0$$

ODE
$x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0$ ODE Classiﬁcation

[[_homogeneous, class G]]

Book solution method
Change of variable

Mathematica
cpu = 0.375388 (sec), leaf count = 74

$\left \{\left \{y(x)\to -\frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{x+i \cosh (c_1)+i \sinh (c_1)}\right \},\left \{y(x)\to \frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{-x+i \cosh (c_1)+i \sinh (c_1)}\right \}\right \}$

Maple
cpu = 0.708 (sec), leaf count = 130

$\left [y \left (x \right ) = -4 x^{2}, y \left (x \right ) = \frac {\left (\sqrt {2}\, \textit {\_C1} -2 x \right ) x \,\textit {\_C1}^{2}}{2 \textit {\_C1}^{2}-4 x^{2}}, y \left (x \right ) = -\frac {\left (\sqrt {2}\, \textit {\_C1} +2 x \right ) x \,\textit {\_C1}^{2}}{2 \left (\textit {\_C1}^{2}-2 x^{2}\right )}, y \left (x \right ) = -\frac {2 x \left (\sqrt {2}\, \textit {\_C1} -x \,\textit {\_C1}^{2}\right )}{\textit {\_C1}^{2} \left (\textit {\_C1}^{2} x^{2}-2\right )}, y \left (x \right ) = \frac {2 x \left (\sqrt {2}\, \textit {\_C1} +x \,\textit {\_C1}^{2}\right )}{\textit {\_C1}^{2} \left (\textit {\_C1}^{2} x^{2}-2\right )}\right ]$ Mathematica raw input

DSolve[-y[x]^3 + x*y[x]^2*y'[x] + x^4*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((x*(Cosh[2*C[1]] + Sinh[2*C[1]]))/(x + I*Cosh[C[1]] + I*Sinh[C[1]]))
}, {y[x] -> (x*(Cosh[2*C[1]] + Sinh[2*C[1]]))/(-x + I*Cosh[C[1]] + I*Sinh[C[1]])
}}

Maple raw input

dsolve(x^4*diff(y(x),x)^2+x*y(x)^2*diff(y(x),x)-y(x)^3 = 0, y(x))

Maple raw output

[y(x) = -4*x^2, y(x) = 1/2*(2^(1/2)*_C1-2*x)/(_C1^2-2*x^2)*x*_C1^2, y(x) = -1/2*
(2^(1/2)*_C1+2*x)/(_C1^2-2*x^2)*x*_C1^2, y(x) = -2*x*(2^(1/2)*_C1-x*_C1^2)/_C1^2
/(_C1^2*x^2-2), y(x) = 2*x*(2^(1/2)*_C1+x*_C1^2)/_C1^2/(_C1^2*x^2-2)]