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 = 0.301641 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {1}{2} \left (x-\sqrt {x \left (x-4 e^{c_1}\right )}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (x+\sqrt {x \left (x-4 e^{c_1}\right )}\right )\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 55
\[\left [y \left (x \right ) = \frac {x \textit {\_C1} -\sqrt {\textit {\_C1}^{2} x^{2}+4 x \textit {\_C1}}}{2 \textit {\_C1}}, y \left (x \right ) = \frac {x \textit {\_C1} +\sqrt {\textit {\_C1}^{2} x^{2}+4 x \textit {\_C1}}}{2 \textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = 1/2/_C1*(x*_C1-(_C1^2*x^2+4*_C1*x)^(1/2)), y(x) = 1/2/_C1*(x*_C1+(_C1^2*x^2+4*_C1*x)^(1/2))]