\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( -3\,x+1 \right ) y \left ( x \right ) }{ \left ( x-1 \right ) \left ( 2\,x-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.051007 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to c_2 \sqrt {1-2 x} (2 x \log (2 (x-1)+1)-2 \log (2 (x-1)+1)-2 x \log (x-1)+2 \log (x-1)-1)-c_1 \sqrt {1-2 x} (x-1)\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {2\,x-1} \left ( x-1 \right ) +{\it \_C2}\, \left ( \left ( 2\,x-2 \right ) \ln \left ( 2\,x- 1 \right ) -1+ \left ( -2\,x+2 \right ) \ln \left ( x-1 \right ) \right ) \sqrt {2\,x-1} \right \} \]