ODE
\[ (y(x)+1) y'(x)=x^2 (1-y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0409178 (sec), leaf count = 61
\[\left \{\left \{y(x)\to 2 W\left (-\frac {1}{2} \sqrt {e^{c_1-\frac {x^3}{3}-1}}\right )+1\right \},\left \{y(x)\to 2 W\left (\frac {1}{2} \sqrt {e^{c_1-\frac {x^3}{3}-1}}\right )+1\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 19
\[ \left \{ {\frac {{x}^{3}}{3}}+y \left ( x \right ) +2\,\ln \left ( y \left ( x \right ) -1 \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[(1 + y[x])*y'[x] == x^2*(1 - y[x]),y[x],x]
Mathematica raw output
{{y[x] -> 1 + 2*ProductLog[-Sqrt[E^(-1 - x^3/3 + C[1])]/2]}, {y[x] -> 1 + 2*ProductLog[Sqrt[E^(-1 - x^3/3 + C[1])]/2]}}
Maple raw input
dsolve((1+y(x))*diff(y(x),x) = x^2*(1-y(x)), y(x),'implicit')
Maple raw output
1/3*x^3+y(x)+2*ln(y(x)-1)+_C1 = 0