4.8.29 \(x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x)\)

ODE
\[ x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0124854 (sec), leaf count = 22

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

Maple
cpu = 0.013 (sec), leaf count = 18

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

DSolve[x*(1 - 2*x^3)*y'[x] == 2*(1 - x^3)*y[x],y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*(-2*x^3+1)*diff(y(x),x) = 2*(-x^3+1)*y(x), y(x),'implicit')

Maple raw output

y(x) = _C1*x^2/(2*x^3-1)^(1/3)