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