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