3.851   ODE No. 851

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

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

Mathematica: cpu = 0.155520 (sec), leaf count = 145 $$\text{Solve}[-\frac{1}{3}(27a+29b{)}^{2/3}\text{RootSum}[{\mathrm{\#}\text{1}}^3(27a+29b{)}^{2/3}-3\mathrm{\#}\text{1}{b}^{2/3}+(27a+29b{)}^{2/3}\mathrm{\&},\frac{\log (\frac{\frac{3ax+b}{b}+3y(x)}{\sqrt[3]{\frac{27a+29b}{b}}}-\mathrm{\#}\text{1})}{b^{2/3}-{\mathrm{\#}\text{1}}^2(27a+29b{)}^{2/3}}\mathrm{\&}]=\frac{1}{9}x{\left(\frac{27a+29b}{b}\right)}^{2/3}+c_1,y(x)]$$

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