4.5.29 \((x+1) y'(x)=y(x) \left (1-x y(x)^3\right )\)

ODE
\[ (x+1) y'(x)=y(x) \left (1-x y(x)^3\right ) \] ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

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

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

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

\[ \left \{ \left (y \relax (x ) \right ) ^{-3}+{\frac {-3\,{x}^{4}-8\,{x}^{3}-6\,{x}^{2}-4\,{\it \_C1}}{4\, \left (1+x \right ) ^{3}}}=0 \right \} \] 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