\[
\boxed{
{x}^{4}{\it d4y} \left( x \right) + \left( 6-4\,a \right) {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) + \left( 4\,{b}^{2}{c}^{2}{x}^{2\,c}+6\, \left( a-1 \right) ^{2}-2\,{c}^{2} \left( {\mu}^{2}+{\nu}^{2} \right) +1 \right) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) + \left( 4\, \left( 3\,c-2\,a+1 \right) {b}^{2}{c}^{2}{x}^{2\,c}+ \left( 2\,a-1 \right)  \left( 2\,{c}^{2} \left( {\mu}^{2}+{\nu}^{2} \right) -2\,a \left( a-1 \right) -1 \right)  \right) x{\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( 4\, \left( a-c \right)  \left( a-2\,c \right) {b}^{2}{c}^{2}{x}^{2\,c}+ \left( c\mu+c\nu+a \right)  \left( c\mu+c\nu-a \right)  \left( c\mu-c\nu+a \right)  \left( c\mu-c\nu-a \right)  \right) y \left( x \right) =0}
\]