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