4.224   ODE No. 1224

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

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

Mathematica: cpu = 0.018002 (sec), leaf count = 30 $$\left\{\{y(x)\to c_2\sin (\sqrt{a}{\sinh }^{-1}(x))+c_1\cos (\sqrt{a}{\sinh }^{-1}(x))\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 23 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left(\sqrt{a}\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{2}\cos \left(\sqrt{a}\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)\right)\}$$