ODE
\[ (x-y(x)) y'(x)=y(x) \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0144344 (sec), leaf count = 20
\[\left \{\left \{y(x)\to -\frac {x}{W\left (-e^{-c_1} x\right )}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 16
\[ \left \{ x- \left ( -\ln \left ( y \left ( x \right ) \right ) +{\it \_C1} \right ) y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[(x - y[x])*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(x/ProductLog[-(x/E^C[1])])}}
Maple raw input
dsolve((x-y(x))*diff(y(x),x) = y(x), y(x),'implicit')
Maple raw output
x-(-ln(y(x))+_C1)*y(x) = 0