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 = 0.0173367 (sec), leaf count = 16
\[\left \{\left \{y(x)\to W\left (x e^{c_1-x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 15
\[ \left \{ x-\ln \left ( x \right ) +y \left ( x \right ) +\ln \left ( y \left ( x \right ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[-((1 - x)*y[x]) + x*(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),'implicit')
Maple raw output
x-ln(x)+y(x)+ln(y(x))+_C1 = 0