4.12   ODE No. 1012

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

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

Mathematica: cpu = 0.007501 (sec), leaf count = 47 $$\left\{\{y(x)\to c_1{D}_{\frac{1}{2}(-a-1)}\left(\sqrt{2}x\right)+c_2{D}_{\frac{a-1}{2}}\left(i\sqrt{2}x\right)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 31 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{M}}_{-\frac{a}{4},\frac{1}{4}}\left(x^2\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{W}}_{-\frac{a}{4},\frac{1}{4}}\left(x^2\right)\frac{1}{\sqrt{x}}\}$$