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 = 0.370791 (sec), leaf count = 137

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

Maple
cpu = 0.378 (sec), leaf count = 102

\[ \left \{ {\it \_C1}+\ln \left (y \relax (x ) -3+x+\sqrt {- \left (y \relax (x ) \right ) ^{2}+ \left (2+2\,x \right ) y \relax (x ) +{x}^{2}-6\,x+1} \right ) =0,\ln \left (y \relax (x ) -3+x+\sqrt {- \left (y \relax (x ) \right ) ^{2}+ \left (2+2\,x \right ) y \relax (x ) +{x}^{2}-6\,x+1} \right ) -2\,\ln \left (2-y \relax (x ) \right ) +{\it \_C1}=0, \left (y \relax (x ) \right ) ^{2}+ \left (-2\,x-2 \right ) y \relax (x ) -{x}^{2}+6\,x-1=0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2+(-2*x-2)*y(x)-x^2+6*x-1 = 0, _C1+ln(y(x)-3+x+(-y(x)^2+(2+2*x)*y(x)+x^2-6*
x+1)^(1/2)) = 0, ln(y(x)-3+x+(-y(x)^2+(2+2*x)*y(x)+x^2-6*x+1)^(1/2))-2*ln(2-y(x)
)+_C1 = 0