5.21   ODE No. 1469

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

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

Mathematica: cpu = 0.027003 (sec), leaf count = 72 $$\left\{\{y(x)\to c_1{e}^{-\frac{a{x}^2}{2}}+c_2{e}^{-\frac{a{x}^2}{2}-\sqrt{3}\sqrt{a}x}+c_3{e}^{\sqrt{3}\sqrt{a}x-\frac{a{x}^2}{2}}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 37 $$\{y\left(x\right)={\mathrm{e}}^{-\frac{a{x}^2}{2}}(\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\sqrt{3}\sqrt{a}x}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-\sqrt{3}\sqrt{a}x})\}$$