\[ y(x) \left (a^2 x \log ^2(x)+a \log (x)+a\right )+(2 a x \log (x)+1) y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0279614 (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 = 0.025 (sec), leaf count = 21
\[y \relax (x ) = x^{-a x} {\mathrm e}^{a x} \left (c_{2} \ln \relax (x )+c_{1}\right )\]