2.1378   ODE No. 1378

\[ y''(x)=-\frac {2 \left (x^2-1\right ) y'(x)}{(x-1)^2 x}-\frac {\left (-2 x^2+2 x+2\right ) y(x)}{(x-1)^2 x^2} \] Mathematica : cpu = 0.0366335 (sec), leaf count = 65


\[\left \{\left \{y(x)\to \frac {c_1 x^2}{1-x}+\frac {c_2 x \left (2 x^2 \log (1-x)-2 x^2 \log (x)+2 x-2 x \log (1-x)+2 x \log (x)-1\right )}{(x-1)^2}\right \}\right \}\] Maple : cpu = 0.034 (sec), leaf count = 48


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