3.414   ODE No. 414

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.639 (sec), leaf count = 337 $$\{{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(y\left(x\right)+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2}){(\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2}+5y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}2\frac{1}{\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}+5\mathit{\_}\mathit{f}}(8{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^3}{{(\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}+5\mathit{\_}\mathit{f})}^2\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}+40{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^3}{{(\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}+5\mathit{\_}\mathit{f})}^2\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-1)d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(-y\left(x\right)+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2}){(-5y\left(x\right)+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\left(y\left(x\right)\right)}^2})}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-2\frac{1}{-5\mathit{\_}\mathit{f}+\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}}(8{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^3}{{(-5\mathit{\_}\mathit{f}+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2})}^2\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\sqrt{-4x^4+{\mathit{\_}\mathit{f}}^2}-40{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^3}{{(-5\mathit{\_}\mathit{f}+\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2})}^2\sqrt{-4{\mathit{\_}\mathit{a}}^4+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-1)d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$