ODE No. 1328

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

✓ Mathematica : cpu = 0.013956 (sec), leaf count = 36

DSolve[Derivative[2][y][x] == (2*y[x])/((-1 + x)^2*x),y[x],x]

\[\left \{\left \{y(x)\to \frac {c_2 \left (-x^2+2 x \log (x)+1\right )}{x-1}-\frac {c_1 x}{x-1}\right \}\right \}\]

✓ Maple : cpu = 0.036 (sec), leaf count = 27

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

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