3.816   ODE No. 816

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

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

Mathematica: cpu = 0.141018 (sec), leaf count = 74 $$\text{Solve}[\frac{1}{2}(\text{RootSum}[{\mathrm{\#}\text{1}}^3-\mathrm{\#}\text{1}+1\mathrm{\&},\frac{\mathrm{\#}\text{1}\log (-\mathrm{\#}\text{1}+x^2-y(x{)}^2)-\log (-\mathrm{\#}\text{1}+x^2-y(x{)}^2)}{3{\mathrm{\#}\text{1}}^2-1}\mathrm{\&}]+x^2)=c_1,y(x)]$$

Maple: cpu = 0.624 (sec), leaf count = 307 $$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{{(\mathit{\_}\mathit{a}-y\left(x\right))}^3{(y\left(x\right)+\mathit{\_}\mathit{a})}^3\mathit{\_}\mathit{a}}{{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^4{\left(y\left(x\right)\right)}^2+3{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^4-{\left(y\left(x\right)\right)}^6-{\mathit{\_}\mathit{a}}^2+{\left(y\left(x\right)\right)}^2+1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-\frac{(-{\mathit{\_}\mathit{f}}^2+x^2-1)\mathit{\_}\mathit{f}}{-{\mathit{\_}\mathit{f}}^6+3{\mathit{\_}\mathit{f}}^4{x}^2-3{\mathit{\_}\mathit{f}}^2{x}^4+x^6+{\mathit{\_}\mathit{f}}^2-x^2+1}-{\int }_{\mathit{\_}\mathit{b}}^x-\frac{{(\mathit{\_}\mathit{a}-\mathit{\_}\mathit{f})}^3{(\mathit{\_}\mathit{f}+\mathit{\_}\mathit{a})}^3\mathit{\_}\mathit{a}(-6{\mathit{\_}\mathit{a}}^4\mathit{\_}\mathit{f}+12{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^3-6{\mathit{\_}\mathit{f}}^5+2\mathit{\_}\mathit{f})}{{({\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^4{\mathit{\_}\mathit{f}}^2+3{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^4-{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{a}}^2+{\mathit{\_}\mathit{f}}^2+1)}^2}-3\frac{{(\mathit{\_}\mathit{a}-\mathit{\_}\mathit{f})}^2{(\mathit{\_}\mathit{f}+\mathit{\_}\mathit{a})}^3\mathit{\_}\mathit{a}}{{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^4{\mathit{\_}\mathit{f}}^2+3{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^4-{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{a}}^2+{\mathit{\_}\mathit{f}}^2+1}+3\frac{{(\mathit{\_}\mathit{a}-\mathit{\_}\mathit{f})}^3{(\mathit{\_}\mathit{f}+\mathit{\_}\mathit{a})}^2\mathit{\_}\mathit{a}}{{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^4{\mathit{\_}\mathit{f}}^2+3{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^4-{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{a}}^2+{\mathit{\_}\mathit{f}}^2+1}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$