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