ODE
\[ (x-2 y(x)) y'(x)=y(x) \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.0178371 (sec), leaf count = 26
\[\left \{\left \{y(x)\to -\frac {x}{2 W\left (-\frac {1}{2} e^{-\frac {c_1}{2}} x\right )}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 16
\[ \left \{ x- \left ( -2\,\ln \left ( y \left ( x \right ) \right ) +{\it \_C1} \right ) y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[(x - 2*y[x])*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> -x/(2*ProductLog[-x/(2*E^(C[1]/2))])}}
Maple raw input
dsolve((x-2*y(x))*diff(y(x),x) = y(x), y(x),'implicit')
Maple raw output
x-(-2*ln(y(x))+_C1)*y(x) = 0