3.339   ODE No. 339

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

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

Mathematica: cpu = 0.109514 (sec), leaf count = 27 $$\text{Solve}[\sqrt{x^2+y(x{)}^2+1}+{\tan }^{-1}\left(\frac{x}{y(x)}\right)=c_1,y(x)]$$

Maple: cpu = 0.140 (sec), leaf count = 27 $$\{\arctan \left(\frac{y\left(x\right)}{x}\right)-\sqrt{x^2+{\left(y\left(x\right)\right)}^2+1}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$