3.336   ODE No. 336

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

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

Mathematica: cpu = 0.063008 (sec), leaf count = 53 $$\text{Solve}[axy(x)+\frac{1}{2}\sqrt{x^2+1}x+\frac{1}{2}(y(x)\sqrt{y(x{)}^2+1}+{\sinh }^{-1}(y(x)))+\frac{1}{2}{\sinh }^{-1}(x)=c_1,y(x)]$$

Maple: cpu = 0.031 (sec), leaf count = 41 $$\{\frac{x}{2}\sqrt{x^2+1}+\frac{\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)}{2}+axy\left(x\right)+\frac{y\left(x\right)}{2}\sqrt{{\left(y\left(x\right)\right)}^2+1}+\frac{\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(y\left(x\right)\right)}{2}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$