3.977   ODE No. 977

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

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

Mathematica: cpu = 0.171522 (sec), leaf count = 139 $$\text{Solve}[-\frac{25}{3}\text{RootSum}[-25{\mathrm{\#}\text{1}}^3+24\sqrt[3]{-1}{5}^{2/3}\mathrm{\#}\text{1}-25\mathrm{\&},\frac{\log (\frac{3e^{2x^2}xy(x)+e^{x^2}x}{5^{2/3}\sqrt[3]{-e^{3x^2}{x}^3}}-\mathrm{\#}\text{1})}{8\sqrt[3]{-1}{5}^{2/3}-25{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1-\frac{5\sqrt[3]{5}{e}^{x^2}{x}^3}{18\sqrt[3]{-e^{3x^2}{x}^3}},y(x)]$$

Maple: cpu = 0.141 (sec), leaf count = 122 $$\{y\left(x\right)=\frac{1}{2{\mathrm{e}}^{x^2}}(\sqrt{11}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-4\sqrt{11}{x}^2+8\sqrt{11}\ln (-\frac{36\sqrt{11}}{11}+36\tan \left(\mathit{\_}\mathit{Z}\right))-4\sqrt{11}\ln (\frac{2592\sqrt{11}{\left({\mathrm{e}}^{x^2}\right)}^2\tan \left(\mathit{\_}\mathit{Z}\right)}{25}-\frac{2592{\mathrm{e}}^{2x^2}\sqrt{11}\tan \left(\mathit{\_}\mathit{Z}\right)}{25}+\frac{14256{\mathrm{e}}^{2x^2}{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}{25}+\frac{2592{\left({\mathrm{e}}^{x^2}\right)}^2}{5}+\frac{1296{\mathrm{e}}^{2x^2}}{25})+4\sqrt{11}\ln \left(11\right)+9\sqrt{11}\mathit{\_}\mathit{C}\mathit{1}-8\mathit{\_}\mathit{Z})\right)-1)\}$$