ODE
\[ x (x-y(x)) y'(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.265246 (sec), leaf count = 20
\[\left \{\left \{y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.176 (sec), leaf count = 21
\[\left [y \left (x \right ) = {\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{-\textit {\_C1}}}{x}\right )-\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[y[x]^2 + x*(x - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x*ProductLog[-(1/(E^C[1]*x))])}}
Maple raw input
dsolve(x*(x-y(x))*diff(y(x),x)+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = exp(-LambertW(-1/x/exp(_C1))-_C1)]