\[ 3 (3 x-1) y'(x)+(3 x-1)^2 y''(x)-9 y(x)-\log ^2(3 x-1)=0 \] ✓ Mathematica : cpu = 0.0975053 (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 = 0.094 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{3\,x-1}}+ \left ( 3\,x-1 \right ) {\it \_C2}-{\frac { \left ( \ln \left ( 3\,x-1 \right ) \right ) ^{2}}{9}}-{\frac {2}{9}} \right \} \]