4.359   ODE No. 1359

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

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

Mathematica: cpu = 0.101513 (sec), leaf count = 86 $$\left\{\{y(x)\to c_1{i}^{-v}{x}^{-v}{}_2{F}_1(\frac{1}{2}-\frac{v}{2},-\frac{v}{2};\frac{1}{2}-v;x^2)+c_2{i}^{v+1}{x}^{v+1}{}_2{F}_1(\frac{v}{2}+\frac{1}{2},\frac{v}{2}+1;v+\frac{3}{2};x^2)\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 57 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(-\frac{v}{2},\frac{1}{2}-\frac{v}{2};\frac{1}{2}-v;x^2)x^{-v}+\mathit{\_}\mathit{C}\mathit{2}{}_2\text{F}{}_1(1+\frac{v}{2},\frac{1}{2}+\frac{v}{2};\frac{3}{2}+v;x^2)x^{v+1}\}$$