2.1245   ODE No. 1245

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

$$-(-n+v+1)(n+v)y(x)-2(n-1)x{y}^{\prime }(x)+(x^2-1)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0161623 (sec), leaf count = 42

$$\left\{\{y(x)\to c_1{(x^2-1)}^{n/2}{P}_v^n(x)+c_2{(x^2-1)}^{n/2}{Q}_v^n(x)\}\right\}$$ ✓ Maple : cpu = 0.306 (sec), leaf count = 27

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