2.822   ODE No. 822

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

$$y^{\prime }(x)=\frac{1}{4}x(-4e^{-x^2}{x}^{2}y(x)+e^{-2x^2}{x}^4-4e^{-x^2}{x}^2+4e^{-x^2}+4y(x{)}^2)$$ ✓ Mathematica : cpu = 0.287834 (sec), leaf count = 32

$$\left\{\{y(x)\to \frac{1}{2}{e}^{-x^2}{x}^2+\frac{1}{-\frac{x^2}{2}+c_1}\}\right\}$$ ✓ Maple : cpu = 0.144 (sec), leaf count = 25

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