4.375   ODE No. 1375

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-2\frac{x(n+1-2a)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{x^2-1}-\frac{(4a{x}^2(a-n)-(x^2-1)(2a+(v-n)(v+n+1)))y\left(x\right)}{{(x^2-1)}^2}=0}}$$

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

Mathematica: cpu = 0.051506 (sec), leaf count = 54 $$\left\{\{y(x)\to c_1{(x^2-1)}^{\frac{1}{2}(2a-n)}{P}_v^n(x)+c_2{(x^2-1)}^{\frac{1}{2}(2a-n)}{Q}_v^n(x)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 39 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x^2-1)}^{a-\frac{n}{2}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(v,n,x)+\mathit{\_}\mathit{C}\mathit{2}{(x^2-1)}^{a-\frac{n}{2}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(v,n,x)\}$$