2.1231   ODE No. 1231

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

$$(x^2-1)y^{″}(x)-v(v+1)y(x)=0$$ ✓ Mathematica : cpu = 0.0577075 (sec), leaf count = 58

$$\left\{\{y(x)\to c_1{}_2{F}_1(-\frac{v}{2}-\frac{1}{2},\frac{v}{2};\frac{1}{2};x^2)+i{c}_{2}x{}_2{F}_1(\frac{v}{2}+\frac{1}{2},-\frac{v}{2};\frac{3}{2};x^2)\}\right\}$$ ✓ Maple : cpu = 0.278 (sec), leaf count = 52

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