4.11.21 \(x (y(x)+1) y'(x)-(1-x) y(x)=0\)

ODE
\[ x (y(x)+1) y'(x)-(1-x) y(x)=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0173367 (sec), leaf count = 16

\[\left \{\left \{y(x)\to W\left (x e^{c_1-x}\right )\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 15

\[ \left \{ x-\ln \relax (x ) +y \relax (x ) +\ln \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[-((1 - x)*y[x]) + x*(1 + y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ProductLog[E^(-x + C[1])*x]}}

Maple raw input

dsolve(x*(1+y(x))*diff(y(x),x)-(1-x)*y(x) = 0, y(x),'implicit')

Maple raw output

x-ln(x)+y(x)+ln(y(x))+_C1 = 0