2.864   ODE No. 864

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

$$y^{\prime }(x)=\frac{e^{\frac{x^2}{4}}y(x)(2e^{-\frac{3x^2}{4}}y(x{)}^2+e^{-\frac{x^2}{2}}xy(x)+e^{-\frac{x^2}{4}}x)}{2e^{-\frac{x^2}{4}}y(x)+2}$$ ✓ Mathematica : cpu = 0.0439594 (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 = 0.092 (sec), leaf count = 186

$$\{y\left(x\right)=1({\mathrm{e}}^{-\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}){\left({\mathrm{e}}^{-\frac{x^2}{4}}\right)}^{-1}{({\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}+{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x})}^{-1},y\left(x\right)=-1({\mathrm{e}}^{-\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}{\mathrm{e}}^{\frac{x^2}{2}}+{\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}){\left({\mathrm{e}}^{-\frac{x^2}{4}}\right)}^{-1}{({\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{2}}-{\mathrm{e}}^{\frac{x^2}{4}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x})}^{-1}\}$$