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