4.53   ODE No. 1053

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

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

Mathematica: cpu = 0.029004 (sec), leaf count = 57 $$\left\{\{y(x)\to c_1{e}^{-\frac{a{x}^2}{2}-\sqrt{a}x}+\frac{c_2{e}^{\sqrt{a}x-\frac{a{x}^2}{2}}}{2\sqrt{a}}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 35 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x}{2}(ax-2\sqrt{a})}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x}{2}(ax+2\sqrt{a})}\}$$