2.718   ODE No. 718

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

$$y^{\prime }(x)=e^{-x^2}x(e^{3x^2}y(x{)}^3+e^{2x^2}y(x{)}^2+1)$$ ✓ Mathematica : cpu = 0.270777 (sec), leaf count = 127

$$\text{Solve}[\frac{11}{3}\text{RootSum}[11{\mathrm{\#}\text{1}}^3+15\sqrt[3]{11}\mathrm{\#}\text{1}+11\mathrm{\&},\frac{\log (\frac{3e^{2x^2}xy(x)+e^{x^2}x}{\sqrt[3]{11}\sqrt[3]{e^{3x^2}{x}^3}}-\mathrm{\#}\text{1})}{11{\mathrm{\#}\text{1}}^2+5\sqrt[3]{11}}\mathrm{\&}]=\frac{{11}^{2/3}{e}^{x^2}{x}^3}{18\sqrt[3]{e^{3x^2}{x}^3}}+c_1,y(x)]$$ ✓ Maple : cpu = 0.184 (sec), leaf count = 44

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