\[
\boxed{
{x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) +6\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) + \left( a{x}^{3}-12 \right) y \left( x \right) =0}
\]