3.756   ODE No. 756

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{2x^{3}y\left(x\right)+x^6+x^2{\left(y\left(x\right)\right)}^2+{\left(y\left(x\right)\right)}^3}{x^4}=0}}$$

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

Mathematica: cpu = 0.080010 (sec), leaf count = 95 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{3y(x)}{x^4}+\frac{1}{x^2}}{\sqrt[3]{29}\sqrt[3]{\frac{1}{x^6}}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{9}{29}^{2/3}{\left(\frac{1}{x^6}\right)}^{2/3}{x}^5,y(x)]$$

Maple: cpu = 0.031 (sec), leaf count = 37 $$\{y\left(x\right)=\frac{(-3+29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-81{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+x+3\mathit{\_}\mathit{C}\mathit{1}))x^2}{9}\}$$