2.414   ODE No. 414

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

$$x^3+x{y}^{\prime }(x{)}^2+y(x)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0892483 (sec), leaf count = 107

$$\{\{y(x)\to x^2\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{5K[1]+\sqrt{K[1{]}^2-4}}dK[1]\mathrm{\&}][{\int }_1^x-\frac{1}{2K[2]}dK[2]+c_1]\},\{y(x)\to x^2\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{\sqrt{K[3{]}^2-4}-5K[3]}dK[3]\mathrm{\&}][{\int }_1^x\frac{1}{2K[4]}dK[4]+c_1]\}\}$$ ✓ Maple : cpu = 0.293 (sec), leaf count = 269

$$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{1}{\mathit{\_}\mathit{a}}(-y\left(x\right)-\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2}){(\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2}+5y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}(-2+(80\mathit{\_}\mathit{f}+16\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}){\int }_{\mathit{\_}\mathit{b}}^x{\mathit{\_}\mathit{a}}^3{(\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}+5\mathit{\_}\mathit{f})}^{-2}\frac{1}{\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}){(\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}+5\mathit{\_}\mathit{f})}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x\frac{1}{\mathit{\_}\mathit{a}}(-y\left(x\right)+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2}){(5y\left(x\right)-\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2})}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}(-2+(-80\mathit{\_}\mathit{f}+16\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}){\int }_{\mathit{\_}\mathit{b}}^x{\mathit{\_}\mathit{a}}^3{(-5\mathit{\_}\mathit{f}+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2})}^{-2}\frac{1}{\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}){(5\mathit{\_}\mathit{f}-\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2})}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$