\[
\boxed{
 \left( x+3 \right) {x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) -3\,x \left( x+2 \right) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +6\, \left( 1+x \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) -6\,y \left( x \right) =0}
\]