##### 4.19.38 $$x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0$$

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

[[_homogeneous, class G], _rational]

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

Mathematica
cpu = 0.623791 (sec), leaf count = 49

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

Maple
cpu = 0.233 (sec), leaf count = 49

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = -2*I/x, y(x) = 2*I/x, y(x) = 2*sinh(-ln(x)+_C1)/x, y(x) = -2*sinh(-ln(x)
+_C1)/x]