4.47   ODE No. 1047

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+4x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(4x^2+2)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.013502 (sec), leaf count = 27 $$\left\{\{y(x)\to c_1{e}^{-x^2}+c_2{e}^{-x^2}x\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 22 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-x^2}+\mathit{\_}\mathit{C}\mathit{2}x{\mathrm{e}}^{-x^2}\}$$