3.906   ODE No. 906

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

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

Mathematica: cpu = 0.055007 (sec), leaf count = 326 $$\{\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},1]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},2]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},3]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},4]\},\{y(x)\to \text{Root}[4{\mathrm{\#}\text{1}}^5-4{\mathrm{\#}\text{1}}^4{c}_1+8{\mathrm{\#}\text{1}}^3{x}^2+{\mathrm{\#}\text{1}}^2(2-8c_1{x}^2)+4\mathrm{\#}\text{1}{x}^4-4c_1{x}^4+2x^2+1\mathrm{\&},5]\}\}$$

Maple: cpu = 0.249 (sec), leaf count = 33 $$\{-\frac{1}{4{({\left(y\left(x\right)\right)}^2+x^2)}^2}-\frac{1}{2{\left(y\left(x\right)\right)}^2+2x^2}-y\left(x\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$