4.209   ODE No. 1209

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

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

Mathematica: cpu = 0.020002 (sec), leaf count = 67 $$\left\{\{y(x)\to \frac{c_1{e}^{-\frac{x^2}{2}}(e^{\frac{x^2}{2}}x-\sqrt{\frac{\pi }{2}}\text{erfi}\left(\frac{x}{\sqrt{2}}\right))}{x^2}+\frac{c_2{e}^{-\frac{x^2}{2}}}{x^2}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 48 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^2}{\mathrm{e}}^{-\frac{x^2}{2}}+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x^2}(-ix\sqrt{\pi }\sqrt{2}+{\mathrm{e}}^{-\frac{x^2}{2}}\pi \mathit{E}\mathit{r}\mathit{f}\left(\frac{i}{2}\sqrt{2}x\right))\}$$