ODE
\[ x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.376055 (sec), leaf count = 25
\[\left \{\left \{y(x)\to -\frac {1}{W\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )}\right \}\right \}\]
Maple ✓
cpu = 0.185 (sec), leaf count = 34
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {x \ln \left (x \right )+\LambertW \left (-\frac {{\mathrm e}^{-\textit {\_C1} +\frac {1}{x}}}{x}\right ) x +x \textit {\_C1} -1}{x}}\right ]\] Mathematica raw input
DSolve[(1 + x)*y[x]^2 + x^2*(1 - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -ProductLog[-(E^(x^(-1) - C[1])/x)]^(-1)}}
Maple raw input
dsolve(x^2*(1-y(x))*diff(y(x),x)+(x+1)*y(x)^2 = 0, y(x))
Maple raw output
[y(x) = exp((x*ln(x)+LambertW(-1/x*exp(-_C1+1/x))*x+x*_C1-1)/x)]