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