##### 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 = 0.292406 (sec), leaf count = 119

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

Maple
cpu = 0.025 (sec), leaf count = 275

$\left [y \left (x \right ) = \frac {4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}} \left (1+x \right )}{3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1}}, y \left (x \right ) = \left (-\frac {4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )}-\frac {i \sqrt {3}\, 4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )}\right ) \left (1+x \right ), y \left (x \right ) = \left (-\frac {4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )}+\frac {i \sqrt {3}\, 4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{6 x^{4}+16 x^{3}+12 x^{2}+8 \textit {\_C1}}\right ) \left (1+x \right )\right ]$ 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))

Maple raw output

[y(x) = 1/(3*x^4+8*x^3+6*x^2+4*_C1)*4^(1/3)*((3*x^4+8*x^3+6*x^2+4*_C1)^2)^(1/3)*
(1+x), y(x) = (-1/2/(3*x^4+8*x^3+6*x^2+4*_C1)*4^(1/3)*((3*x^4+8*x^3+6*x^2+4*_C1)
^2)^(1/3)-1/2*I*3^(1/2)/(3*x^4+8*x^3+6*x^2+4*_C1)*4^(1/3)*((3*x^4+8*x^3+6*x^2+4*
_C1)^2)^(1/3))*(1+x), y(x) = (-1/2/(3*x^4+8*x^3+6*x^2+4*_C1)*4^(1/3)*((3*x^4+8*x
^3+6*x^2+4*_C1)^2)^(1/3)+1/2*I*3^(1/2)/(3*x^4+8*x^3+6*x^2+4*_C1)*4^(1/3)*((3*x^4
+8*x^3+6*x^2+4*_C1)^2)^(1/3))*(1+x)]