4.239   ODE No. 1239

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

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

Mathematica: cpu = 0.014002 (sec), leaf count = 46 $$\left\{\{y(x)\to c_1{P}_{\frac{1}{2}(\sqrt{4l+1}-1)}(x)+c_2{Q}_{\frac{1}{2}(\sqrt{4l+1}-1)}(x)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 35 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(\frac{1}{2}\sqrt{1+4l}-\frac{1}{2},x)+\mathit{\_}\mathit{C}\mathit{2}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(\frac{1}{2}\sqrt{1+4l}-\frac{1}{2},x)\}$$