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