2.698   ODE No. 698

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

$$y^{\prime }(x)=e^x(e^{-3x}y(x{)}^3+e^{-2x}y(x{)}^2+1)$$ ✓ Mathematica : cpu = 0.252682 (sec), leaf count = 108

$$\text{Solve}[-\frac{19}{3}\text{RootSum}[-19{\mathrm{\#}\text{1}}^3+6\sqrt[3]{38}\mathrm{\#}\text{1}-19\mathrm{\&},\frac{\log (\frac{3e^{-2x}y(x)+e^{-x}}{\sqrt[3]{38}\sqrt[3]{e^{-3x}}}-\mathrm{\#}\text{1})}{2\sqrt[3]{38}-19{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=\frac{1}{9}{38}^{2/3}{e}^{2x}{\left(e^{-3x}\right)}^{2/3}x+c_1,y(x)]$$ ✓ Maple : cpu = 0.265 (sec), leaf count = 34

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