4.34.49 \(\left (1-2 x^3\right ) y''(x)+6 x^2 y'(x)-6 x y(x)=0\)

ODE
\[ \left (1-2 x^3\right ) y''(x)+6 x^2 y'(x)-6 x y(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.968556 (sec), leaf count = 19

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

Maple
cpu = 0.022 (sec), leaf count = 14

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

DSolve[-6*x*y[x] + 6*x^2*y'[x] + (1 - 2*x^3)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x*C[1] - (1 + x^3)*C[2]}}

Maple raw input

dsolve((-2*x^3+1)*diff(diff(y(x),x),x)+6*x^2*diff(y(x),x)-6*x*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C2*x^3+_C1*x+_C2