2.1359   ODE No. 1359

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

$$y^{″}(x)=-\frac{v(v+1)y(x)}{x^2(x^2-1)}-\frac{2x{y}^{\prime }(x)}{x^2-1}$$ ✓ Mathematica : cpu = 0.102466 (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 = 0.092 (sec), leaf count = 57

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(-\frac{v}{2},\frac{1}{2}-\frac{v}{2};\frac{1}{2}-v;x^2)x^{-v}+\mathit{\_}\mathit{C}\mathit{2}{}_2\text{F}{}_1(1+\frac{v}{2},\frac{1}{2}+\frac{v}{2};\frac{3}{2}+v;x^2)x^{v+1}\}$$