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

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0170666 (sec), leaf count = 23

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

Maple
cpu = 0.008 (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