2.1336   ODE No. 1336

\[ y''(x)=-\frac {(1-3 x) y(x)}{(x-1) (2 x-1)^2} \]

✓ Mathematica : cpu = 0.0327586 (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 = 0.049 (sec), leaf count = 42

dsolve(diff(diff(y(x),x),x) = -(-3*x+1)/(x-1)/(2*x-1)^2*y(x),y(x))
 

\[y \left (x \right ) = \left (-2 c_{2} \left (x -1\right ) \ln \left (2 x -1\right )+2 c_{2} \left (x -1\right ) \ln \left (x -1\right )+x c_{1} -c_{1} +c_{2} \right ) \sqrt {2 x -1}\]