##### 4.14.6 $$3 x y(x)^2 y'(x)=2 x-y(x)^3$$

ODE
$3 x y(x)^2 y'(x)=2 x-y(x)^3$ ODE Classiﬁcation

[[_homogeneous, class G], _exact, _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.304255 (sec), leaf count = 72

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

Maple
cpu = 0.032 (sec), leaf count = 99

$\left [y \left (x \right ) = \frac {\left (\left (x^{2}+\textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{x}, y \left (x \right ) = -\frac {\left (\left (x^{2}+\textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{2 x}-\frac {i \sqrt {3}\, \left (\left (x^{2}+\textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{2 x}, y \left (x \right ) = -\frac {\left (\left (x^{2}+\textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{2 x}+\frac {i \sqrt {3}\, \left (\left (x^{2}+\textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{2 x}\right ]$ Mathematica raw input

DSolve[3*x*y[x]^2*y'[x] == 2*x - y[x]^3,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(3*x*y(x)^2*diff(y(x),x) = 2*x-y(x)^3, y(x))

Maple raw output

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