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 = 0.176871 (sec), leaf count = 23
\[\left \{\left \{y(x)\to 1+W\left (\frac {e^{-x-1+c_1}}{x-1}\right )\right \}\right \}\]
Maple ✓
cpu = 0.062 (sec), leaf count = 22
\[\left [y \left (x \right ) = \LambertW \left (\frac {{\mathrm e}^{-x -1}}{\textit {\_C1} \left (x -1\right )}\right )+1\right ]\] 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))
Maple raw output
[y(x) = LambertW(1/_C1/(x-1)*exp(-x-1))+1]