4.5.50 \(3 x y'(x)=y(x) \left (x y(x)^3+2\right )\)

ODE
\[ 3 x y'(x)=y(x) \left (x y(x)^3+2\right ) \] ODE Classification

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00875218 (sec), leaf count = 84

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

Maple
cpu = 0.005 (sec), leaf count = 17

\[ \left \{ \left (y \relax (x ) \right ) ^{-3}+{\frac {x}{3}}-{\frac {{\it \_C1}}{{x}^{2}}}=0 \right \} \] Mathematica raw input

DSolve[3*x*y'[x] == y[x]*(2 + x*y[x]^3),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(3*x*diff(y(x),x) = (2+x*y(x)^3)*y(x), y(x),'implicit')

Maple raw output

1/y(x)^3+1/3*x-1/x^2*_C1 = 0