4.5.29 $(x+1)y^{\prime }(x)=y(x)(1-xy(x{)}^3)$

ODE
$$(x+1)y^{\prime }(x)=y(x)(1-xy(x{)}^3)$$ ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.0139653 (sec), leaf count = 119

$$\{\{y(x)\to -\frac{(-2{)}^{2/3}(x+1)}{\sqrt[3]{-4c_1-3x^4-8x^3-6x^2}}\},\{y(x)\to -\frac{2^{2/3}(x+1)}{\sqrt[3]{-4c_1-3x^4-8x^3-6x^2}}\},\{y(x)\to \frac{\sqrt[3]{-1}{2}^{2/3}(x+1)}{\sqrt[3]{-4c_1-3x^4-8x^3-6x^2}}\}\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 34

$$\{{\left(y\left(x\right)\right)}^{-3}+\frac{-3x^4-8x^3-6x^2-4\mathit{\_}\mathit{C}\mathit{1}}{4{(1+x)}^3}=0\}$$ Mathematica raw input

DSolve[(1 + x)*y'[x] == y[x]*(1 - x*y[x]^3),y[x],x]

Mathematica raw output

{{y[x] -> -(((-2)^(2/3)*(1 + x))/(-6*x^2 - 8*x^3 - 3*x^4 - 4*C[1])^(1/3))}, {y[x
] -> -((2^(2/3)*(1 + x))/(-6*x^2 - 8*x^3 - 3*x^4 - 4*C[1])^(1/3))}, {y[x] -> ((-
1)^(1/3)*2^(2/3)*(1 + x))/(-6*x^2 - 8*x^3 - 3*x^4 - 4*C[1])^(1/3)}}

Maple raw input

dsolve((1+x)*diff(y(x),x) = (1-x*y(x)^3)*y(x), y(x),'implicit')

Maple raw output

1/y(x)^3+1/4*(-3*x^4-8*x^3-6*x^2-4*_C1)/(1+x)^3 = 0