3.927   ODE No. 927

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-1/8(-8{\mathrm{e}}^{-x^2}+8x^2{\mathrm{e}}^{-x^2}-8-8{\left(y\left(x\right)\right)}^2+8x^2{\mathrm{e}}^{-x^2}y\left(x\right)-2x^4{\left({\mathrm{e}}^{-x^2}\right)}^2-8{\left(y\left(x\right)\right)}^3+12x^2{\mathrm{e}}^{-x^2}{\left(y\left(x\right)\right)}^2-6y\left(x\right)x^4{\left({\mathrm{e}}^{-x^2}\right)}^2+x^6{\left({\mathrm{e}}^{-x^2}\right)}^3)x=0}}$$

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

Mathematica: cpu = 0.139518 (sec), leaf count = 112 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{1}{2}{e}^{-x^2}x(2e^{x^2}-3x^2)+3xy(x)}{\sqrt[3]{29}\sqrt[3]{x^3}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{18}{29}^{2/3}{\left(x^3\right)}^{2/3},y(x)]$$

Maple: cpu = 0.078 (sec), leaf count = 72 $$\{y\left(x\right)=-\frac{-9x^2{\mathrm{e}}^{-x^2}+6{\mathrm{e}}^{-x^2}{\mathrm{e}}^{x^2}-58\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x^2-162{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+6\mathit{\_}\mathit{C}\mathit{1})}{18{\mathrm{e}}^{-x^2}{\mathrm{e}}^{x^2}}\}$$