4.247   ODE No. 1247

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

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

Mathematica: cpu = 0.224528 (sec), leaf count = 97 $$\left\{\{y(x)\to c_1\sqrt{1-x^2}{(x^2-1)}^{-a/2}{e}^{-\sqrt{(a-1{)}^2}{\tanh }^{-1}(x)}+\frac{c_2\sqrt{1-x^2}{(x^2-1)}^{-a/2}{e}^{\sqrt{(a-1{)}^2}{\tanh }^{-1}(x)}}{2\sqrt{(a-1{)}^2}}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 27 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(1+x)}^{1-a}+\mathit{\_}\mathit{C}\mathit{2}{(x-1)}^{1-a}\}$$