4.18.13 $$y(x) y'(x)+x y'(x)^2-y(x)^4=0$$

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

[[_homogeneous, class G]]

Book solution method
No Missing Variables ODE, Solve for $$x$$

Mathematica
cpu = 0.518883 (sec), leaf count = 25

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

Maple
cpu = 1.152 (sec), leaf count = 95

$\left [y \left (x \right ) = -\frac {1}{2 \sqrt {-x}}, y \left (x \right ) = \frac {1}{2 \sqrt {-x}}, y \left (x \right ) = -\frac {\sqrt {-x \left (\tanh ^{2}\left (-\frac {\ln \left (x \right )}{2}+\frac {\textit {\_C1}}{2}\right )-1\right )}}{2 x \tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {\textit {\_C1}}{2}\right )}, y \left (x \right ) = \frac {\sqrt {-x \left (\tanh ^{2}\left (-\frac {\ln \left (x \right )}{2}+\frac {\textit {\_C1}}{2}\right )-1\right )}}{2 x \tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {\textit {\_C1}}{2}\right )}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (2*E^(C[1]/2))/(E^C[1] - 4*x)}}

Maple raw input

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

Maple raw output

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