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