3.570   ODE No. 570

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

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

Mathematica: cpu = 0.108514 (sec), leaf count = 29 $$\text{DSolve}[(y^{\prime }(x{)}^2+1)(ax+{\tan }^{-1}(y^{\prime }(x)))+y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 0.047 (sec), leaf count = 30 $$\{y\left(x\right)=\int \tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(ax{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{Z}+ax+\tan \left(\mathit{\_}\mathit{Z}\right)+\mathit{\_}\mathit{Z})\right)\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1}\}$$