2.1375   ODE No. 1375

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

$$y^{″}(x)=-\frac{y(x)(4a{x}^2(a-n)-(x^2-1)(2a+(v-n)(n+v+1)))}{{(x^2-1)}^2}-\frac{2x(-2a+n+1)y^{\prime }(x)}{x^2-1}$$ ✓ Mathematica : cpu = 0.0520915 (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 = 0.079 (sec), leaf count = 39

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x^2-1)}^{a-\frac{n}{2}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(v,n,x)+\mathit{\_}\mathit{C}\mathit{2}{(x^2-1)}^{a-\frac{n}{2}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(v,n,x)\}$$