3.626   ODE No. 626

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

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

Mathematica: cpu = 0.195525 (sec), leaf count = 104 $$\text{Solve}[\frac{1}{2}(\log \left(\frac{-\sqrt{x^2+1}y(x{)}^2-(x^2+1)y(x)+{(x^2+1)}^{3/2}}{{(x^2+1)}^{3/2}}\right)+\log (x^2+1))=c_1+\frac{{\tanh }^{-1}\left(\frac{3\sqrt{x^2+1}+y(x)}{\sqrt{5}(\sqrt{x^2+1}+y(x))}\right)}{\sqrt{5}},y(x)]$$

Maple: cpu = 0.359 (sec), leaf count = 112 $$\{-\frac{4}{3}\ln \left(36\frac{\sqrt{x^2+1}}{y\left(x\right)+\sqrt{x^2+1}}\right)+\frac{2}{3}\ln (-\frac{1296}{11}(y\left(x\right)\sqrt{x^2+1}-x^2+{\left(y\left(x\right)\right)}^2-1){(y\left(x\right)+\sqrt{x^2+1})}^{-2})-\frac{4\sqrt{5}}{15}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{\sqrt{5}}{5}(3\sqrt{x^2+1}+y\left(x\right)){(y\left(x\right)+\sqrt{x^2+1})}^{-1}\right)+\frac{2\ln (x^2+1)}{3}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$