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