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 = 0.28418 (sec), leaf count = 137

$$\{\{y(x)\to \frac{2e^{\frac{x^2}{2}}}{-2e^{\frac{x^2}{4}}+\sqrt{2}\sqrt{2e^{\frac{x^2}{2}}+2e^{\frac{x^2}{2}}(-2x+c_1)}}\},\{y(x)\to -\frac{2e^{\frac{x^2}{2}}}{2e^{\frac{x^2}{4}}+\sqrt{2}\sqrt{2e^{\frac{x^2}{2}}+2e^{\frac{x^2}{2}}(-2x+c_1)}}\}\}$$ ✓ Maple : cpu = 0.145 (sec), leaf count = 162

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