2.1041   ODE No. 1041

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

$$(n+1)y(x)+y^{″}(x)+x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0102891 (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 = 0.071 (sec), leaf count = 47

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^2}{2}}\mathit{M}(-\frac{n}{2}+\frac{1}{2},\frac{3}{2},\frac{x^2}{2})x+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x^2}{2}}\mathit{U}(-\frac{n}{2}+\frac{1}{2},\frac{3}{2},\frac{x^2}{2})x\}$$