4.11.50 \(x (x-2 y(x)) y'(x)+y(x)^2=0\)

ODE
\[ x (x-2 y(x)) y'(x)+y(x)^2=0 \] ODE Classification

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type``class B`]]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.0221595 (sec), leaf count = 51

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

Maple
cpu = 0.011 (sec), leaf count = 23

\[ \left \{ -{\it \_C1}+\ln \left (-{\frac { \left (x-y \relax (x ) \right ) y \relax (x ) }{{x}^{2}}} \right ) +\ln \relax (x ) =0 \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

-_C1+ln(-y(x)*(x-y(x))/x^2)+ln(x) = 0