2.697   ODE No. 697

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

$$y^{\prime }(x)=e^{2x/3}(e^{-2x}y(x{)}^3+e^{-4x/3}y(x{)}^2+1)$$ ✓ Mathematica : cpu = 0.259811 (sec), leaf count = 114

$$\text{Solve}[-\frac{35}{3}\text{RootSum}[-35{\mathrm{\#}\text{1}}^3+9\sqrt[3]{35}\mathrm{\#}\text{1}-35\mathrm{\&},\frac{\log (\frac{3e^{-4x/3}y(x)+e^{-2x/3}}{\sqrt[3]{35}\sqrt[3]{e^{-2x}}}-\mathrm{\#}\text{1})}{3\sqrt[3]{35}-35{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=\frac{1}{9}{35}^{2/3}{e}^{4x/3}{\left(e^{-2x}\right)}^{2/3}x+c_1,y(x)]$$ ✓ Maple : cpu = 0.28 (sec), leaf count = 40

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