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