\[ y''(x)=\frac {y(x)}{3 (x-2) x^2}+\frac {(6 x-1) y'(x)}{3 (x-2) x} \] ✓ Mathematica : cpu = 0.0394114 (sec), leaf count = 40
DSolve[Derivative[2][y][x] == y[x]/(3*(-2 + x)*x^2) + ((-1 + 6*x)*Derivative[1][y][x])/(3*(-2 + x)*x),y[x],x]
\[\left \{\left \{y(x)\to \frac {3}{935} c_2 x \left (18 x^2-102 x+187\right )+c_1 \sqrt [6]{x} (2-x)^{17/6}\right \}\right \}\] ✓ Maple : cpu = 0.026 (sec), leaf count = 27
dsolve(diff(diff(y(x),x),x) = 1/3/x*(6*x-1)/(x-2)*diff(y(x),x)+1/3/x^2/(x-2)*y(x),y(x))
\[y \left (x \right ) = c_{2} \left (x -2\right )^{\frac {17}{6}} x^{\frac {1}{6}}+18 \left (x^{2}-\frac {17}{3} x +\frac {187}{18}\right ) c_{1} x\]