3.982   ODE No. 982

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

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

Mathematica: cpu = 0.104513 (sec), leaf count = 132 $$\text{Solve}[-\frac{7}{3}\text{RootSum}[-7{\mathrm{\#}\text{1}}^3+6\sqrt[3]{-7}\mathrm{\#}\text{1}-7\mathrm{\&},\frac{\log (\frac{3e^{-\frac{x^2}{2}}y(x)+e^{-\frac{x^2}{4}}}{\sqrt[3]{7}\sqrt[3]{-e^{-\frac{3x^2}{4}}}}-\mathrm{\#}\text{1})}{2\sqrt[3]{-7}-7{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{9}{7}^{2/3}{e}^{\frac{x^2}{2}}{(-e^{-\frac{3x^2}{4}})}^{2/3}x,y(x)]$$

Maple: cpu = 0.312 (sec), leaf count = 187 $$\{-\frac{2}{3}\ln (18y\left(x\right){\mathrm{e}}^{-1/2x^2}{\mathrm{e}}^{1/4x^2}+6{\mathrm{e}}^{-1/4x^2}{\mathrm{e}}^{1/4x^2}-6)+\frac{1}{3}\ln (\frac{324{\left(y\left(x\right)\right)}^2}{7}{\left({\mathrm{e}}^{-\frac{x^2}{2}}\right)}^2{\left({\mathrm{e}}^{\frac{x^2}{4}}\right)}^2+\frac{216y\left(x\right)}{7}{\mathrm{e}}^{-\frac{x^2}{2}}{\left({\mathrm{e}}^{\frac{x^2}{4}}\right)}^2{\mathrm{e}}^{-\frac{x^2}{4}}+\frac{36}{7}{\left({\mathrm{e}}^{-\frac{x^2}{4}}\right)}^2{\left({\mathrm{e}}^{\frac{x^2}{4}}\right)}^2+\frac{108y\left(x\right)}{7}{\mathrm{e}}^{\frac{x^2}{4}}{\mathrm{e}}^{-\frac{x^2}{2}}+\frac{36}{7}{\mathrm{e}}^{-\frac{x^2}{4}}{\mathrm{e}}^{\frac{x^2}{4}}+36)+\frac{2\sqrt{3}}{9}\arctan \left(\frac{\sqrt{3}}{9}(6y\left(x\right){\mathrm{e}}^{-1/2x^2}{\mathrm{e}}^{1/4x^2}+2{\mathrm{e}}^{-1/4x^2}{\mathrm{e}}^{1/4x^2}+1)\right)+\frac{2x}{3}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$