2.851   ODE No. 851

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

$$y^{\prime }(x)=\frac{a^3{x}^3+3a^{2}b{x}^{2}y(x)+a^{2}b{x}^2+3a{b}^{2}xy(x{)}^2+2a{b}^{2}xy(x)+b^{3}y(x{)}^3+b^{3}y(x{)}^2+b^3}{b^3}$$ ✓ Mathematica : cpu = 0.171457 (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 = 0.068 (sec), leaf count = 42

$$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{({\mathit{\_}\mathit{a}}^{3}b+{\mathit{\_}\mathit{a}}^{2}b+a+b)}^{-1}d\mathit{\_}\mathit{a}b-x+\mathit{\_}\mathit{C}\mathit{1})b-ax}{b}\}$$