3.801   ODE No. 801

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

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

Mathematica: cpu = 0.101013 (sec), leaf count = 126 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{3e^{-\frac{x^2}{2}}y(x)+e^{-\frac{x^2}{4}}}{\sqrt[3]{29}\sqrt[3]{e^{-\frac{3x^2}{4}}}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{9}{29}^{2/3}{e}^{\frac{x^2}{2}}{\left(e^{-\frac{3x^2}{4}}\right)}^{2/3}x,y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 63 $$\{y\left(x\right)=-\frac{1}{9}(3{\mathrm{e}}^{-1/4x^2}{\mathrm{e}}^{1/4x^2}-29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-81{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+x+3\mathit{\_}\mathit{C}\mathit{1})){\left({\mathrm{e}}^{\frac{x^2}{4}}\right)}^{-1}{\left({\mathrm{e}}^{-\frac{x^2}{2}}\right)}^{-1}\}$$