ODE
\[ x (1-y(x)) y'(x)+(x+1) y(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0170666 (sec), leaf count = 23
\[\left \{\left \{y(x)\to -W\left (-\frac {e^{-c_1-x}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.008 (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