3.890   ODE No. 890

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{x}{-y\left(x\right)+1+{\left(y\left(x\right)\right)}^4+2x^2{\left(y\left(x\right)\right)}^2+x^4+{\left(y\left(x\right)\right)}^6+3x^2{\left(y\left(x\right)\right)}^4+3x^4{\left(y\left(x\right)\right)}^2+x^6}=0}}$$

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

Mathematica: cpu = 0.140518 (sec), leaf count = 103 $$\text{Solve}[y(x)-\frac{1}{2}\text{RootSum}[{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^{2}y(x{)}^2+{\mathrm{\#}\text{1}}^2+3\mathrm{\#}\text{1}y(x{)}^4+2\mathrm{\#}\text{1}y(x{)}^2+y(x{)}^6+y(x{)}^4+1\mathrm{\&},\frac{\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2+6\mathrm{\#}\text{1}y(x{)}^2+2\mathrm{\#}\text{1}+3y(x{)}^4+2y(x{)}^2}\mathrm{\&}]=c_1,y(x)]$$

Maple: cpu = 0.686 (sec), leaf count = 34 $$\{-y\left(x\right)+\frac{{\int }^{{\left(y\left(x\right)\right)}^2+x^2}{({\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{a}}^2+1)}^{-1}d\mathit{\_}\mathit{a}}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$