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