\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-2\,{\frac { \left ( {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( x-1 \right ) ^{2}}}-{\frac { \left ( -2\,{x}^{2}+2\,x+2 \right ) y \left ( x \right ) }{{x}^{2} \left ( x-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.049506 (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 = 0.031 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{x-1}}+{ \frac {{\it \_C2}\,x}{ \left ( x-1 \right ) ^{2}} \left ( \left ( -{x}^{2 }+x \right ) \ln \left ( x-1 \right ) + \left ( {x}^{2}-x \right ) \ln \left ( x \right ) -x+{\frac {1}{2}} \right ) } \right \} \]