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