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