4.10.15 \((x-2 y(x)) y'(x)=y(x)\)

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

\[ \left \{ x- \left (-2\,\ln \left (y \relax (x ) \right ) +{\it \_C1} \right ) y \relax (x ) =0 \right \} \] 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