3.718   ODE No. 718

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

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

Mathematica: cpu = 0.129517 (sec), leaf count = 127 $$\text{Solve}[\frac{11}{3}\text{RootSum}[11{\mathrm{\#}\text{1}}^3+15\sqrt[3]{11}\mathrm{\#}\text{1}+11\mathrm{\&},\frac{\log (\frac{3e^{2x^2}xy(x)+e^{x^2}x}{\sqrt[3]{11}\sqrt[3]{e^{3x^2}{x}^3}}-\mathrm{\#}\text{1})}{11{\mathrm{\#}\text{1}}^2+5\sqrt[3]{11}}\mathrm{\&}]=c_1+\frac{{11}^{2/3}{e}^{x^2}{x}^3}{18\sqrt[3]{e^{3x^2}{x}^3}},y(x)]$$

Maple: cpu = 0.063 (sec), leaf count = 44 $$\{y\left(x\right)=-\frac{11\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-5x^2+20250{\int }^{\mathit{\_}\mathit{Z}}{(121{\mathit{\_}\mathit{a}}^3+3375\mathit{\_}\mathit{a}-3375)}^{-1}d\mathit{\_}\mathit{a}+6\mathit{\_}\mathit{C}\mathit{1})+15}{45{\mathrm{e}}^{x^2}}\}$$