4.41   ODE No. 1041

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(n+1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.008501 (sec), leaf count = 55 $$\left\{\{y(x)\to c_1{e}^{-\frac{x^2}{2}}{H}_n\left(\frac{x}{\sqrt{2}}\right)+c_2{e}^{-\frac{x^2}{2}}{}_1{F}_1(-\frac{n}{2};\frac{1}{2};\frac{x^2}{2})\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 47 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^2}{2}}\mathit{M}(-\frac{n}{2}+\frac{1}{2},\frac{3}{2},\frac{x^2}{2})x+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x^2}{2}}\mathit{U}(-\frac{n}{2}+\frac{1}{2},\frac{3}{2},\frac{x^2}{2})x\}$$