3.864   ODE No. 864

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)({\left({\mathrm{e}}^{-1/4x^2}\right)}^{2}xy\left(x\right)+{\mathrm{e}}^{-1/4x^2}x+2{\left(y\left(x\right)\right)}^2{\mathrm{e}}^{-3/4x^2}){\mathrm{e}}^{1/4x^2}}{2y\left(x\right){\mathrm{e}}^{-1/4x^2}+2}=0}}$$

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

Mathematica: cpu = 0.041005 (sec), leaf count = 137 $$\{\{y(x)\to \frac{2e^{\frac{x^2}{2}}}{\sqrt{2}\sqrt{2e^{\frac{x^2}{2}}(c_1-2x)+2e^{\frac{x^2}{2}}}-2e^{\frac{x^2}{4}}}\},\{y(x)\to -\frac{2e^{\frac{x^2}{2}}}{\sqrt{2}\sqrt{2e^{\frac{x^2}{2}}(c_1-2x)+2e^{\frac{x^2}{2}}}+2e^{\frac{x^2}{4}}}\}\}$$

Maple: cpu = 0.062 (sec), leaf count = 186 $$\{y\left(x\right)=1({\mathrm{e}}^{-\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}){\left({\mathrm{e}}^{-\frac{x^2}{4}}\right)}^{-1}{({\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}+{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x})}^{-1},y\left(x\right)=-1({\mathrm{e}}^{-\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}{\mathrm{e}}^{\frac{x^2}{2}}+{\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}){\left({\mathrm{e}}^{-\frac{x^2}{4}}\right)}^{-1}{({\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x})}^{-1}\}$$