\[
\boxed{
x \left( y \left( x \right) \ln  \left( xy \left( x \right)  \right) +y \left( x \right) -ax \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) -y \left( x \right)  \left( ax\ln  \left( xy \left( x \right)  \right) -y \left( x \right) +ax \right) =0}
\]