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

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0157774 (sec), leaf count = 21

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

Maple
cpu = 0.007 (sec), leaf count = 17

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