\[ y''(x)=\frac {2 y(x)}{(x-1)^2 x} \] ✓ Mathematica : cpu = 0.0224098 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {c_2 \left (-x^2+2 x \log (x)+1\right )}{x-1}-\frac {c_1 x}{x-1}\right \}\right \}\]
✓ Maple : cpu = 0.031 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,x}{x-1}}+{\frac {{\it \_C2}\, \left ( 2\,x\ln \left ( x \right ) -{x}^{2}+1 \right ) }{x-1}} \right \} \]