\[ \boxed { \left ( 3\,x-1 \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\, \left ( 3\,x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -9\,y \left ( x \right ) - \left ( \ln \left ( 3\,x-1 \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.103013 (sec), leaf count = 101 \[ \left \{\left \{y(x)\to \frac {c_1 \left ((1-3 x)^2+1\right )}{2 (1-3 x)}+\frac {i c_2 \left ((1-3 x)^2-1\right )}{2 (1-3 x)}+\frac {-6 x-3 x \log ^2(3 x-1)+\log ^2(3 x-1)+\log (3 x-1)-\log (1-3 x)+1}{9 (3 x-1)}\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{3\,x-1}}+ \left ( 3\,x -1 \right ) {\it \_C2}-{\frac { \left ( \ln \left ( 3\,x-1 \right ) \right ) ^{2}}{9}}-{\frac {2}{9}} \right \} \]