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