\[ y''(x)=-\frac {(1-3 x) y(x)}{(x-1) (2 x-1)^2} \] ✓ Mathematica : cpu = 0.0428465 (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 = 0.039 (sec), leaf count = 44
\[\left \{y \left (x \right ) = \left (c_{1} x -2 c_{2} \left (x -1\right ) \ln \left (x -1\right )+2 c_{2} \left (x -1\right ) \ln \left (2 x -1\right )-c_{1}-c_{2}\right ) \sqrt {2 x -1}\right \}\]