\[ y''(x)=-\frac {2 \left (x^2-1\right ) y'(x)}{(x-1)^2 x}-\frac {\left (-2 x^2+2 x+2\right ) y(x)}{(x-1)^2 x^2} \] ✓ Mathematica : cpu = 0.0383291 (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 = 0.06 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) ={\frac {x}{ \left ( x-1 \right ) ^{2}} \left ( -{\it \_C2}\,x \left ( x-1 \right ) \ln \left ( x-1 \right ) +{\it \_C2}\,x \left ( x-1 \right ) \ln \left ( x \right ) +{\it \_C1}\,{x}^{2}+ \left ( -{\it \_C1}-{\it \_C2} \right ) x+{\frac {{\it \_C2}}{2}} \right ) } \right \} \]