2.626   ODE No. 626

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

$$y^{\prime }(x)=\frac{x}{\sqrt{x^2+1}+y(x)}$$ ✓ Mathematica : cpu = 0.150483 (sec), leaf count = 88

$$\text{Solve}[\frac{1}{2}(\log (-\frac{y(x{)}^2}{x^2+1}-\frac{y(x)}{\sqrt{x^2+1}}+1)+\log (x^2+1))=\frac{{\tanh }^{-1}\left(\frac{3\sqrt{x^2+1}+y(x)}{\sqrt{5}(\sqrt{x^2+1}+y(x))}\right)}{\sqrt{5}}+c_1,y(x)]$$ ✓ Maple : cpu = 1.107 (sec), leaf count = 115

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