\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =2\,{\frac {y \left ( x \right ) }{x \left ( x-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.022003 (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 = 0.015 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {x{\it \_C1}}{x-1}}+{\frac {{\it \_C2}\, \left ( 2\,x\ln \left ( x \right ) -{x}^{2}+1 \right ) }{x-1}} \right \} \]