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