\[ (3 x-1)^2 y''(x)+3 (3 x-1) y'(x)-9 y(x)-\log ^2(3 x-1)=0 \] ✓ Mathematica : cpu = 0.0860394 (sec), leaf count = 101
\[\left \{\left \{y(x)\to \frac {-6 x-3 x \log ^2(3 x-1)+\log ^2(3 x-1)+\log (3 x-1)-\log (1-3 x)+1}{9 (3 x-1)}+\frac {c_1 \left ((1-3 x)^2+1\right )}{2 (1-3 x)}+\frac {i c_2 \left ((1-3 x)^2-1\right )}{2 (1-3 x)}\right \}\right \}\] ✓ Maple : cpu = 0.018 (sec), leaf count = 32
\[y \relax (x ) = \frac {c_{1}}{3 x -1}+\left (3 x -1\right ) c_{2}-\frac {\ln \left (3 x -1\right )^{2}}{9}-\frac {2}{9}\]