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 = 0.206958 (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 = 0.144 (sec), leaf count = 31
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {x \ln \left (x \right )-\LambertW \left (-x \,{\mathrm e}^{\textit {\_C1} +\frac {1}{x}}\right ) x +x \textit {\_C1} +1}{x}}\right ]\] 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))
Maple raw output
[y(x) = exp((x*ln(x)-LambertW(-x*exp(_C1+1/x))*x+x*_C1+1)/x)]