\[ y(x) \left (a^2 x \log ^2(x)+a \log (x)+a\right )+(2 a x \log (x)+1) y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0414915 (sec), leaf count = 25
\[\left \{\left \{y(x)\to e^{a x} x^{-a x} \left (c_2 \log (x)+c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.021 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={x}^{-ax}{{\rm e}^{ax}} \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \]