\[ (3 x-1)^2 y''(x)+3 (3 x-1) y'(x)-9 y(x)-\log ^2(3 x-1)=0 \] ✓ Mathematica : cpu = 0.111073 (sec), leaf count = 80
\[\left \{\left \{y(x)\to \frac {-81 c_1 x^2-81 i c_2 x^2+54 c_1 x+54 i c_2 x-18 c_1-12 x+(2-6 x) \log ^2(3 x-1)-2 \log (1-3 x)+2 \log (3 x-1)+2}{54 x-18}\right \}\right \}\]
✓ Maple : cpu = 0.023 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{3\,x-1}}+ \left ( 3\,x-1 \right ) {\it \_C2}-{\frac { \left ( \ln \left ( 3\,x-1 \right ) \right ) ^{2}}{9}}-{\frac {2}{9}} \right \} \]