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