3.693   ODE No. 693

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

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

Mathematica: cpu = 0.173022 (sec), leaf count = 146 $$\text{Solve}[-\frac{1}{3}(9b+29{)}^{2/3}\text{RootSum}[{\mathrm{\#}\text{1}}^3(9b+29{)}^{2/3}-9\mathrm{\#}\text{1}b-3\mathrm{\#}\text{1}+(9b+29{)}^{2/3}\mathrm{\&},\frac{\log (\frac{3e^{-2bx}y(x)+e^{-bx}}{\sqrt[3]{(9b+29)e^{-3bx}}}-\mathrm{\#}\text{1})}{{\mathrm{\#}\text{1}}^2(-(9b+29{)}^{2/3})+3b+1}\mathrm{\&}]=\frac{1}{9}x{e}^{2bx}{((9b+29)e^{-3bx})}^{2/3}+c_1,y(x)]$$

Maple: cpu = 0.078 (sec), leaf count = 40 $$\{y\left(x\right)=\frac{1}{{\mathrm{e}}^{-bx}}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x-{\int }^{\mathit{\_}\mathit{Z}}-{({\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}b+1)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\}$$