3.822   ODE No. 822

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/4(4{\mathrm{e}}^{-x^2}-4x^2{\mathrm{e}}^{-x^2}+4{\left(y\left(x\right)\right)}^2-4x^2{\mathrm{e}}^{-x^2}y\left(x\right)+x^4{\left({\mathrm{e}}^{-x^2}\right)}^2)x=0}}$$

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

Mathematica: cpu = 0.042005 (sec), leaf count = 32 $$\left\{\{y(x)\to \frac{1}{c_1-\frac{x^2}{2}}+\frac{1}{2}{e}^{-x^2}{x}^2\}\right\}$$

Maple: cpu = 0.109 (sec), leaf count = 25 $$\{y\left(x\right)=\frac{x^2{\mathrm{e}}^{-x^2}}{2}+{(\mathit{\_}\mathit{C}\mathit{1}-\frac{x^2}{2})}^{-1}\}$$