\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 2\,ax\ln \left ( x \right ) +1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {a}^{2}x \left ( \ln \left ( x \right ) \right ) ^{2}+a\ln \left ( x \right ) +a \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.038505 (sec), leaf count = 36 \[ \left \{\left \{y(x)\to c_1 e^{a x} x^{-a x}+c_2 e^{a x} x^{-a x} \log (x)\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-ax}{{\rm e}^{ax}}+{\it \_C2}\,{x}^{-ax}{{\rm e}^{ax}}\ln \left ( x \right ) \right \} \]