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