4.13   ODE No. 1013

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

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

Mathematica: cpu = 0.019502 (sec), leaf count = 43 $$\left\{\{y(x)\to c_1{D}_{-1}\left(\sqrt{2}\sqrt{a}x\right)+c_2{D}_0\left(i\sqrt{2}\sqrt{a}x\right)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 29 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{a{x}^2}{2}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{a{x}^2}{2}}\mathit{E}\mathit{r}\mathit{f}\left(\sqrt{a}x\right)\}$$