\[ y''(x)=-\frac {2 \left (x^2-1\right ) y'(x)}{(x-1)^2 x}-\frac {\left (-2 x^2+2 x+2\right ) y(x)}{(x-1)^2 x^2} \] ✓ Mathematica : cpu = 0.0393729 (sec), leaf count = 65
\[\left \{\left \{y(x)\to \frac {c_1 x^2}{1-x}+\frac {c_2 x \left (2 x^2 \log (1-x)-2 x^2 \log (x)+2 x-2 x \log (1-x)+2 x \log (x)-1\right )}{(x-1)^2}\right \}\right \}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 48
\[\left \{y \left (x \right ) = \frac {\left (c_{1} x^{2}+c_{2} \left (x -1\right ) x \ln \left (x \right )-c_{2} \left (x -1\right ) x \ln \left (x -1\right )+\frac {c_{2}}{2}+\left (-c_{1}-c_{2}\right ) x \right ) x}{\left (x -1\right )^{2}}\right \}\]