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