3.852   ODE No. 852

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{\alpha }^3+{\left(y\left(x\right)\right)}^2{\alpha }^3+2y\left(x\right){\alpha }^2\beta x+\alpha {\beta }^2{x}^2+{\left(y\left(x\right)\right)}^3{\alpha }^3+3{\left(y\left(x\right)\right)}^2{\alpha }^2\beta x+3y\left(x\right)\alpha {\beta }^2{x}^2+{\beta }^3{x}^3}{{\alpha }^3}=0}}$$

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

Mathematica: cpu = 0.149019 (sec), leaf count = 145 $$\text{Solve}[-\frac{1}{3}(29\alpha +27\beta {)}^{2/3}\text{RootSum}[{\mathrm{\#}\text{1}}^3(29\alpha +27\beta {)}^{2/3}-3\mathrm{\#}\text{1}{\alpha }^{2/3}+(29\alpha +27\beta {)}^{2/3}\mathrm{\&},\frac{\log (\frac{\frac{\alpha +3\beta x}{\alpha }+3y(x)}{\sqrt[3]{\frac{29\alpha +27\beta }{\alpha }}}-\mathrm{\#}\text{1})}{{\alpha }^{2/3}-{\mathrm{\#}\text{1}}^2(29\alpha +27\beta {)}^{2/3}}\mathrm{\&}]=\frac{1}{9}x{\left(\frac{29\alpha +27\beta }{\alpha }\right)}^{2/3}+c_1,y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 42 $$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{({\mathit{\_}\mathit{a}}^3\alpha +{\mathit{\_}\mathit{a}}^2\alpha +\alpha +\beta )}^{-1}d\mathit{\_}\mathit{a}\alpha -x+\mathit{\_}\mathit{C}\mathit{1})\alpha -\beta x}{\alpha }\}$$