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