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