4.374   ODE No. 1374

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

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

Mathematica: cpu = 0.036005 (sec), leaf count = 32 $$\left\{\{y(x)\to c_1{(x^2-1)}^a{P}_v(x)+c_2{(x^2-1)}^a{Q}_v(x)\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 29 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x^2-1)}^a\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(v,x)+\mathit{\_}\mathit{C}\mathit{2}{(x^2-1)}^a\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(v,x)\}$$