3.73   ODE No. 73

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

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

Mathematica: cpu = 1.032631 (sec), leaf count = 733 $$\text{Solve}[\frac{3(\text{a0}+y(x)(\text{a1}+y(x)(\text{a2}+\text{a3}y(x))){)}^{2/3}(y(x)-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1])F_1(\frac{5}{3};-\frac{2}{3},-\frac{2}{3};\frac{8}{3};\frac{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-y(x)}{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},2]},\frac{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-y(x)}{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},3]})}{5{\left(\frac{y(x)-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},2]}{\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1]-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},2]}\right)}^{2/3}{\left(\frac{y(x)-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},3]}{\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1]-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},3]}\right)}^{2/3}}=\frac{3(\text{a0}+x(\text{a1}+x(\text{a2}+\text{a3}x)){)}^{2/3}(x-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1])F_1(\frac{5}{3};-\frac{2}{3},-\frac{2}{3};\frac{8}{3};\frac{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-x}{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},2]},\frac{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-x}{\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},1]-\text{Root}[\text{a3}{\mathrm{\#}\text{1}}^3+\text{a2}{\mathrm{\#}\text{1}}^2+\text{a1}\mathrm{\#}\text{1}+\text{a0}\mathrm{\&},3]})}{5{\left(\frac{x-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},2]}{\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1]-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},2]}\right)}^{2/3}{\left(\frac{x-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},3]}{\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1]-\text{Root}[{\mathrm{\#}\text{1}}^3\text{a3}+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},3]}\right)}^{2/3}}+c_1,y(x)]$$

Maple: cpu = 0.187 (sec), leaf count = 91 $$\{{\int }^{y\left(x\right)}{({\mathit{\_}\mathit{a}}^3\mathit{a}\mathit{3}+{\mathit{\_}\mathit{a}}^2\mathit{a}\mathit{2}+\mathit{\_}\mathit{a}\mathit{a}\mathit{1}+\mathit{a}\mathit{0})}^{\frac{2}{3}}d\mathit{\_}\mathit{a}+{\int }^x-{\left(\frac{{\mathit{\_}\mathit{a}}^3\mathit{a}\mathit{3}+{\mathit{\_}\mathit{a}}^2\mathit{a}\mathit{2}+\mathit{\_}\mathit{a}\mathit{a}\mathit{1}+\mathit{a}\mathit{0}}{\mathit{a}\mathit{3}{\left(y\left(x\right)\right)}^3+\mathit{a}\mathit{2}{\left(y\left(x\right)\right)}^2+\mathit{a}\mathit{1}y\left(x\right)+\mathit{a}\mathit{0}}\right)}^{\frac{2}{3}}{(\mathit{a}\mathit{3}{\left(y\left(x\right)\right)}^3+\mathit{a}\mathit{2}{\left(y\left(x\right)\right)}^2+\mathit{a}\mathit{1}y\left(x\right)+\mathit{a}\mathit{0})}^{\frac{2}{3}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$