3.557   ODE No. 557

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

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

Mathematica: cpu = 0.016002 (sec), leaf count = 39 $$\{\{y(x)\to -\sqrt{c_{1}x-x^2}\},\{y(x)\to \sqrt{c_{1}x-x^2}\}\}$$

Maple: cpu = 0.093 (sec), leaf count = 78 $$\{\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt{\frac{{({\left(y\left(x\right)\right)}^2+x^2)}^2}{x^2{\left(y\left(x\right)\right)}^2}}}{(-\frac{x^2-{\left(y\left(x\right)\right)}^2}{2xy\left(x\right)}+\frac{1}{2}\sqrt{\frac{x^4+2x^2{\left(y\left(x\right)\right)}^2+{\left(y\left(x\right)\right)}^4}{x^2{\left(y\left(x\right)\right)}^2}})}^{-1}+x=0\}$$