4.246   ODE No. 1246

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

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

Mathematica: cpu = 0.021003 (sec), leaf count = 42 $$\left\{\{y(x)\to c_1{(x^2-1)}^{v/2}{P}_v^v(x)+c_2{(x^2-1)}^{v/2}{Q}_v^v(x)\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 35 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x^2-1)}^v+\mathit{\_}\mathit{C}\mathit{2}{(x^2-1)}^{v}x{}_2\text{F}{}_1(\frac{1}{2},v+1;\frac{3}{2};x^2)\}$$