4.12.24 \(x^2 (1-y(x)) y'(x)+(1-x) y(x)=0\)

ODE
\[ x^2 (1-y(x)) y'(x)+(1-x) y(x)=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0167342 (sec), leaf count = 21

\[\left \{\left \{y(x)\to -W\left (x \left (-e^{\frac {1}{x}-c_1}\right )\right )\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 17

\[ \left \{ {x}^{-1}+\ln \relax (x ) +y \relax (x ) -\ln \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[(1 - x)*y[x] + x^2*(1 - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^2*(1-y(x))*diff(y(x),x)+(1-x)*y(x) = 0, y(x),'implicit')

Maple raw output

1/x+ln(x)+y(x)-ln(y(x))+_C1 = 0