2.570   ODE No. 570

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

$$(y^{\prime }(x{)}^2+1)(ax+{\tan }^{-1}(y^{\prime }(x)))+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 1.46901 (sec), leaf count = 51

$$\text{Solve}[\{y(x)=\frac{1}{a({\text{K}\mathrm{\$}\text{137866}}^2+1)}+c_1,x=\frac{{\text{K}\mathrm{\$}\text{137866}}^2(-{\tan }^{-1}(\text{K}\mathrm{\$}\text{137866}))-\text{K}\mathrm{\$}\text{137866}-{\tan }^{-1}(\text{K}\mathrm{\$}\text{137866})}{a({\text{K}\mathrm{\$}\text{137866}}^2+1)}\},\{y(x),\text{K}\mathrm{\$}\text{137866}\}]$$ ✓ Maple : cpu = 0.09 (sec), leaf count = 30

$$\{y\left(x\right)=\int \tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(ax{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{Z}+ax+\tan \left(\mathit{\_}\mathit{Z}\right)+\mathit{\_}\mathit{Z})\right)\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1}\}$$