5.6   ODE No. 1454

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+2ax\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+ay\left(x\right)=0}}$$

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

Mathematica: cpu = 0.009001 (sec), leaf count = 79 $$\left\{\{y(x)\to c_1\text{Ai}{\left(\sqrt[3]{-\frac{1}{2}}\sqrt[3]{a}x\right)}^2+c_3\text{Bi}{\left(\sqrt[3]{-\frac{1}{2}}\sqrt[3]{a}x\right)}^2+c_2\text{Ai}\left(\sqrt[3]{-\frac{1}{2}}\sqrt[3]{a}x\right)\text{Bi}\left(\sqrt[3]{-\frac{1}{2}}\sqrt[3]{a}x\right)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 55 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\left(\mathrm{A}\mathrm{i}(-\frac{2^{\frac{2}{3}}x}{2}\sqrt[3]{a})\right)}^2+\mathit{\_}\mathit{C}\mathit{2}{\left(\mathrm{B}\mathrm{i}(-\frac{2^{\frac{2}{3}}x}{2}\sqrt[3]{a})\right)}^2+\mathit{\_}\mathit{C}\mathit{3}\mathrm{A}\mathrm{i}(-\frac{2^{\frac{2}{3}}x}{2}\sqrt[3]{a})\mathrm{B}\mathrm{i}(-\frac{2^{\frac{2}{3}}x}{2}\sqrt[3]{a})\}$$