3.905   ODE No. 905

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

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

Mathematica: cpu = 0.060508 (sec), leaf count = 85 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{ax+3}{ax}+3y(x)}{\sqrt[3]{29}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{9}{29}^{2/3}x,y(x)]$$

Maple: cpu = 0.031 (sec), leaf count = 46 $$\{y\left(x\right)=\frac{29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-81{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+x+3\mathit{\_}\mathit{C}\mathit{1})ax-3ax-9}{9ax}\}$$