4.9.36 \((y(x)+1) y'(x)=x^2 (1-y(x))\)

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

\[ \left \{ {\frac {{x}^{3}}{3}}+y \relax (x ) +2\,\ln \left (y \relax (x ) -1 \right ) +{\it \_C1}=0 \right \} \] 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*Prod
uctLog[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