3.896   ODE No. 896

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

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

Mathematica: cpu = 0.201026 (sec), leaf count = 106 $$\text{Solve}[\frac{1}{2}\text{RootSum}[-{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^{2}y(x{)}^2+{\mathrm{\#}\text{1}}^2-3\mathrm{\#}\text{1}y(x{)}^4-2\mathrm{\#}\text{1}y(x{)}^2+y(x{)}^6+y(x{)}^4+1\mathrm{\&},\frac{\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2-6\mathrm{\#}\text{1}y(x{)}^2-2\mathrm{\#}\text{1}+3y(x{)}^4+2y(x{)}^2}\mathrm{\&}]-x=c_1,y(x)]$$

Maple: cpu = 0.296 (sec), leaf count = 63 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{\mathit{\_}\mathit{a}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^4{x}^2-3{\mathit{\_}\mathit{a}}^2{x}^4+x^6-{\mathit{\_}\mathit{a}}^4+2{\mathit{\_}\mathit{a}}^2{x}^2-x^4-1}\mathrm{d}\mathit{\_}\mathit{a}+x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$