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