\[ y(x) \left (a^2 x \log ^2(x)+a \log (x)+a\right )+(2 a x \log (x)+1) y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0403187 (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 = 0.02 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-ax}{{\rm e}^{ax}}+{\it \_C2}\,{x}^{-ax}{{\rm e}^{ax}}\ln \left ( x \right ) \right \} \]