\[ y''(x)=\frac {(5 x-4) y'(x)}{(x-1) x}-\frac {(9 x-6) y(x)}{(x-1) x^2} \] ✓ Mathematica : cpu = 0.0203757 (sec), leaf count = 25
DSolve[Derivative[2][y][x] == -(((-6 + 9*x)*y[x])/((-1 + x)*x^2)) + ((-4 + 5*x)*Derivative[1][y][x])/((-1 + x)*x),y[x],x]
\[\left \{\left \{y(x)\to c_1 x^3-c_2 x^2 (x \log (x)+1)\right \}\right \}\] ✓ Maple : cpu = 0.019 (sec), leaf count = 18
dsolve(diff(diff(y(x),x),x) = 1/x*(5*x-4)/(x-1)*diff(y(x),x)-(9*x-6)/x^2/(x-1)*y(x),y(x))
\[y \left (x \right ) = x^{2} \left (\ln \left (x \right ) c_{2} x +c_{1} x +c_{2}\right )\]