3.39   ODE No. 39

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

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

Mathematica: cpu = 0.051007 (sec), leaf count = 54 $$\text{Solve}[\text{RootSum}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},\frac{\log (y(x)-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2\text{a3}+2\mathrm{\#}\text{1}\text{a2}+\text{a1}}\mathrm{\&}]=c_1+x,y(x)]$$

Maple: cpu = 0.016 (sec), leaf count = 30 $$\{x-{\int }^{y\left(x\right)}{({\mathit{\_}\mathit{a}}^3\mathit{a}\mathit{3}+{\mathit{\_}\mathit{a}}^2\mathit{a}\mathit{2}+\mathit{\_}\mathit{a}\mathit{a}\mathit{1}+\mathit{a}\mathit{0})}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0.228 (sec), leaf count = 0 $$[\int \frac{1}{a_{3}y{\left(x\right)}^3+a_{2}y{\left(x\right)}^2+a_{1}y\left(x\right)+a_0}d\left(y\left(x\right)\right)=c+x,\mathtt{\text{separable}}]$$