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