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 = 0.177507 (sec), leaf count = 21
\[\left \{\left \{y(x)\to -W\left (-\frac {e^{x-c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 15
\[\left [y \left (x \right ) = -\LambertW \left (-\frac {{\mathrm e}^{x} \textit {\_C1}}{x}\right )\right ]\] 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))
Maple raw output
[y(x) = -LambertW(-exp(x)*_C1/x)]