\[
\boxed{
{x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) +3\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) + \left( 4\,{a}^{2}{x}^{2\,a}+1-4\,{\nu}^{2}{a}^{2} \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) =4\,{a}^{3}{x}^{2\,a-1}y \left( x \right) =0}
\]