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