\[
\boxed{
{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) -{\frac { \left( 3\,n+4 \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) }{n}}-2\,{\frac { \left( n+1 \right)  \left( n+2 \right) y \left( x \right) }{{n}^{2}} \left(  \left( y \left( x \right)  \right) ^{{\frac {n}{n+1}}}-1 \right) }=0}
\]