2.977   ODE No. 977

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

$$y^{\prime }(x)=e^{2x^2}xy(x)(e^{-x^2}y(x)+e^{-2x^2}+y(x{)}^2)$$ ✓ Mathematica : cpu = 0.198181 (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 = 0.209 (sec), leaf count = 122

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