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 = 0.162036 (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 = 0.072 (sec), leaf count = 17
\[\left [y \left (x \right ) = {\mathrm e}^{\LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {\textit {\_C1}}{2}}}{2}\right )+\frac {\textit {\_C1}}{2}}\right ]\] Mathematica raw input
DSolve[(x - 2*y[x])*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> -1/2*x/ProductLog[-1/2*x/E^(C[1]/2)]}}
Maple raw input
dsolve((x-2*y(x))*diff(y(x),x) = y(x), y(x))
Maple raw output
[y(x) = exp(LambertW(-1/2*x*exp(-1/2*_C1))+1/2*_C1)]