##### 4.18.22 $$x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0$$

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

[[_homogeneous, class A], _rational, _dAlembert]

Book solution method
Change of variable

Mathematica
cpu = 0.242924 (sec), leaf count = 51

$\left \{\left \{y(x)\to -e^{-c_1} x^2+x-\frac {e^{c_1}}{2}\right \},\left \{y(x)\to -\frac {1}{2} e^{c_1} x^2+x-e^{-c_1}\right \}\right \}$

Maple
cpu = 0.083 (sec), leaf count = 52

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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