ODE
\[ (1-x) y(x) y'(x)+x (1-y(x))=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0207448 (sec), leaf count = 23
\[\left \{\left \{y(x)\to W\left (\frac {e^{c_1-x-1}}{x-1}\right )+1\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 17
\[ \left \{ x+\ln \left ( -1+x \right ) +y \left ( x \right ) +\ln \left ( y \left ( x \right ) -1 \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*(1 - y[x]) + (1 - x)*y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 1 + ProductLog[E^(-1 - x + C[1])/(-1 + x)]}}
Maple raw input
dsolve(y(x)*(1-x)*diff(y(x),x)+x*(1-y(x)) = 0, y(x),'implicit')
Maple raw output
x+ln(-1+x)+y(x)+ln(y(x)-1)+_C1 = 0