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 = 0.187563 (sec), leaf count = 61

\[\left \{\left \{y(x)\to 1+2 W\left (-\frac {1}{2} \sqrt {e^{-\frac {x^3}{3}-1+c_1}}\right )\right \},\left \{y(x)\to 1+2 W\left (\frac {1}{2} \sqrt {e^{-\frac {x^3}{3}-1+c_1}}\right )\right \}\right \}\]

Maple ✓
cpu = 0.084 (sec), leaf count = 20

\[\left [y \left (x \right ) = 2 \LambertW \left (\frac {\textit {\_C1} \,{\mathrm e}^{-\frac {x^{3}}{6}-\frac {1}{2}}}{2}\right )+1\right ]\] 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[-1/2*Sqrt[E^(-1 - x^3/3 + C[1])]]}, {y[x] -> 1 + 2*Pr
oductLog[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))

Maple raw output

[y(x) = 2*LambertW(1/2*_C1*exp(-1/6*x^3-1/2))+1]