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 = 0.16854 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1 x^2}{\sqrt [3]{1-2 x^3}}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,x^{2}}{\left (2 x^{3}-1\right )^{\frac {1}{3}}}\right ]\] 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))
Maple raw output
[y(x) = _C1*x^2/(2*x^3-1)^(1/3)]