3.413   ODE No. 413

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

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

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

Maple: cpu = 0.640 (sec), leaf count = 337 $$\{{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(y\left(x\right)+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2}){(\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2}+4y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-2\frac{1}{\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}+4\mathit{\_}\mathit{f}}(6{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^2}{{(\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}+4\mathit{\_}\mathit{f})}^2\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}+24{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^2}{{(\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}+4\mathit{\_}\mathit{f})}^2\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}+1)d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(-y\left(x\right)+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2}){(-4y\left(x\right)+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2})}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}2\frac{1}{-4\mathit{\_}\mathit{f}+\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}}(6{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^2}{{(-4\mathit{\_}\mathit{f}+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2})}^2\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}-24{\int }_{\mathit{\_}\mathit{b}}^x\frac{{\mathit{\_}\mathit{a}}^2}{{(-4\mathit{\_}\mathit{f}+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2})}^2\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}+1)d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$