2.816   ODE No. 816

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

$$y^{\prime }(x)=\frac{x(x-y(x){)}^3(y(x)+x{)}^3}{y(x)(x^2-y(x{)}^2-1)}$$ ✓ Mathematica : cpu = 0.17209 (sec), leaf count = 72

$$\text{Solve}[\text{RootSum}[{\mathrm{\#}\text{1}}^3-\mathrm{\#}\text{1}+1\mathrm{\&},\frac{\mathrm{\#}\text{1}\log (-\mathrm{\#}\text{1}+x^2-y(x{)}^2)-\log (-\mathrm{\#}\text{1}+x^2-y(x{)}^2)}{3{\mathrm{\#}\text{1}}^2-1}\mathrm{\&}]+x^2=2c_1,y(x)]$$

✓ Maple : cpu = 0.925 (sec), leaf count = 190

$$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{{(\mathit{\_}\mathit{a}-y\left(x\right))}^3{(y\left(x\right)+\mathit{\_}\mathit{a})}^3\mathit{\_}\mathit{a}}{{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^4{\left(y\left(x\right)\right)}^2+3{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^4-{\left(y\left(x\right)\right)}^6-{\mathit{\_}\mathit{a}}^2+{\left(y\left(x\right)\right)}^2+1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-\frac{(-{\mathit{\_}\mathit{f}}^2+x^2-1)\mathit{\_}\mathit{f}}{-{\mathit{\_}\mathit{f}}^6+3{\mathit{\_}\mathit{f}}^4{x}^2-3{\mathit{\_}\mathit{f}}^2{x}^4+x^6+{\mathit{\_}\mathit{f}}^2-x^2+1}-{\int }_{\mathit{\_}\mathit{b}}^{x}4\frac{\mathit{\_}\mathit{a}{(\mathit{\_}\mathit{f}+\mathit{\_}\mathit{a})}^2({\mathit{\_}\mathit{a}}^2-{\mathit{\_}\mathit{f}}^2-3/2)\mathit{\_}\mathit{f}{(\mathit{\_}\mathit{a}-\mathit{\_}\mathit{f})}^2}{{({\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^4{\mathit{\_}\mathit{f}}^2+(3{\mathit{\_}\mathit{f}}^4-1){\mathit{\_}\mathit{a}}^2-{\mathit{\_}\mathit{f}}^6+{\mathit{\_}\mathit{f}}^2+1)}^2}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$