\[ y''(x)=-\frac {(1-3 x) y(x)}{(x-1) (2 x-1)^2} \] ✓ Mathematica : cpu = 0.037068 (sec), leaf count = 70
DSolve[Derivative[2][y][x] == -(((1 - 3*x)*y[x])/((-1 + x)*(-1 + 2*x)^2)),y[x],x]
\[\left \{\left \{y(x)\to c_2 \sqrt {1-2 x} (2 x \log (2 (x-1)+1)-2 \log (2 (x-1)+1)-2 x \log (x-1)+2 \log (x-1)-1)-c_1 \sqrt {1-2 x} (x-1)\right \}\right \}\] ✓ Maple : cpu = 0.033 (sec), leaf count = 42
dsolve(diff(diff(y(x),x),x) = -(-3*x+1)/(x-1)/(2*x-1)^2*y(x),y(x))
\[y \left (x \right ) = \left (-2 c_{2} \left (x -1\right ) \ln \left (2 x -1\right )+2 c_{2} \left (x -1\right ) \ln \left (x -1\right )+c_{1} x -c_{1}+c_{2}\right ) \sqrt {2 x -1}\]