2.557   ODE No. 557

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

$$x(y^{\prime }(x)+\sqrt{y^{\prime }(x{)}^2+1})-y(x)=0$$ ✓ Mathematica : cpu = 0.0181082 (sec), leaf count = 39

$$\{\{y(x)\to -\sqrt{c_{1}x-x^2}\},\{y(x)\to \sqrt{c_{1}x-x^2}\}\}$$

✓ Maple : cpu = 0.448 (sec), leaf count = 78

$$\{\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt{\frac{{({\left(y\left(x\right)\right)}^2+x^2)}^2}{x^2{\left(y\left(x\right)\right)}^2}}}{(-\frac{x^2-{\left(y\left(x\right)\right)}^2}{2xy\left(x\right)}+\frac{1}{2}\sqrt{\frac{x^4+2x^2{\left(y\left(x\right)\right)}^2+{\left(y\left(x\right)\right)}^4}{x^2{\left(y\left(x\right)\right)}^2}})}^{-1}+x=0\}$$