##### 4.20.9 $$(2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0$$

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

[[_homogeneous, class C], _dAlembert]

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

Mathematica
cpu = 0.480871 (sec), leaf count = 137

$\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {-e^{c_1} \left (4 x-4+e^{c_1}\right )}+2-\frac {e^{c_1}}{2}\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {-e^{c_1} \left (4 x-4+e^{c_1}\right )}+4-e^{c_1}\right )\right \},\left \{y(x)\to -\sqrt {-e^{c_1} \left (2 x-2+e^{c_1}\right )}+2-e^{c_1}\right \},\left \{y(x)\to \sqrt {-e^{c_1} \left (2 x-2+e^{c_1}\right )}+2-e^{c_1}\right \}\right \}$

Maple
cpu = 1.928 (sec), leaf count = 78

$\left [y \left (x \right ) = -\sqrt {2}\, x +\sqrt {2}+x +1, y \left (x \right ) = \sqrt {2}\, x -\sqrt {2}+x +1, y \left (x \right ) = 2+\frac {\textit {\_C1}}{2}-\frac {\sqrt {-\textit {\_C1}^{2}+4 \textit {\_C1} \left (x -1\right )}}{2}, y \left (x \right ) = 2+\textit {\_C1} -\sqrt {-\textit {\_C1}^{2}+2 \textit {\_C1} \left (x -1\right )}\right ]$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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