2.339   ODE No. 339

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

$$(x\sqrt{x^2+y(x{)}^2+1}-y(x)(x^2+y(x{)}^2))y^{\prime }(x)-\sqrt{x^2+y(x{)}^2+1}y(x)-x(x^2+y(x{)}^2)=0$$ ✓ Mathematica : cpu = 0.337253 (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 = 0.138 (sec), leaf count = 27

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