\[ y''(x)=\frac {y(x)}{3 (x-2) x^2}+\frac {(6 x-1) y'(x)}{3 (x-2) x} \] ✓ Mathematica : cpu = 0.0670709 (sec), leaf count = 40
\[\left \{\left \{y(x)\to \frac {3}{935} c_2 x \left (18 x^2-102 x+187\right )+c_1 \sqrt [6]{x} (2-x)^{17/6}\right \}\right \}\]
✓ Maple : cpu = 0.039 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( 18\,{x}^{3}-102\,{x}^{2}+187\,x \right ) +{\it \_C2}\, \left ( x-2 \right ) ^{{\frac {17}{6}}}\sqrt [6]{x} \right \} \]