ODE
\[ x (y(x)+1) y'(x)-(1-x) y(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.1746 (sec), leaf count = 16
\[\left \{\left \{y(x)\to W\left (x e^{-x+c_1}\right )\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 14
\[\left [y \left (x \right ) = \LambertW \left (\frac {{\mathrm e}^{-x} x}{\textit {\_C1}}\right )\right ]\] 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)]