4.36.7 \(x^5 y''(x)-\left (1-2 x^3\right ) x y'(x)+\left (1-2 x^3\right ) y(x)=0\)

ODE
\[ x^5 y''(x)-\left (1-2 x^3\right ) x y'(x)+\left (1-2 x^3\right ) y(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0297923 (sec), leaf count = 22

\[\left \{\left \{y(x)\to x \left (c_2 e^{-\frac {1}{3 x^3}}+c_1\right )\right \}\right \}\]

Maple
cpu = 0.042 (sec), leaf count = 16

\[ \left \{ y \left ( x \right ) =x \left ( {{\rm e}^{-{\frac {1}{3\,{x}^{3}}}}}{\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input

DSolve[(1 - 2*x^3)*y[x] - x*(1 - 2*x^3)*y'[x] + x^5*y''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^5*diff(diff(y(x),x),x)-x*(-2*x^3+1)*diff(y(x),x)+(-2*x^3+1)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x*(exp(-1/3/x^3)*_C2+_C1)