##### 4.20.29 $$y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0$$

ODE
$y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0$ ODE Classiﬁcation

[_quadrature]

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

Mathematica
cpu = 0.177426 (sec), leaf count = 72

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

Maple
cpu = 0.062 (sec), leaf count = 45

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

DSolve[x - (1 + x)*y[x]*y'[x] + y[x]^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(y(x)^2*diff(y(x),x)^2-(x+1)*y(x)*diff(y(x),x)+x = 0, y(x))

Maple raw output

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