4.378   ODE No. 1378

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-2\frac{(x^2-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{x{(x-1)}^2}-\frac{(-2x^2+2x+2)y\left(x\right)}{x^2{(x-1)}^2}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.049506 (sec), leaf count = 65 $$\left\{\{y(x)\to \frac{c_1{x}^2}{1-x}+\frac{c_{2}x(2x^2\log (1-x)-2x^2\log (x)+2x-2x\log (1-x)+2x\log (x)-1)}{(x-1{)}^2}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 50 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^2}{x-1}+\frac{\mathit{\_}\mathit{C}\mathit{2}x}{{(x-1)}^2}((-x^2+x)\ln (x-1)+(x^2-x)\ln \left(x\right)-x+\frac{1}{2})\}$$