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 = 0.014677 (sec), leaf count = 20
\[\left \{\left \{y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 26
\[ \left \{ -\ln \left ( {\frac {y \left ( x \right ) }{x}} \right ) +{\frac {y \left ( x \right ) }{x}}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
-ln(y(x)/x)+y(x)/x-ln(x)-_C1 = 0