3.369   ODE No. 369

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

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

Mathematica: cpu = 0.046506 (sec), leaf count = 107 $$\{\{y(x)\to -\frac{a\tan (x-c_1)}{\sqrt{{\tan }^2(x-c_1)+1}}\},\{y(x)\to \frac{a\tan (x-c_1)}{\sqrt{{\tan }^2(x-c_1)+1}}\},\{y(x)\to -\frac{a\tan (c_1+x)}{\sqrt{{\tan }^2(c_1+x)+1}}\},\{y(x)\to \frac{a\tan (c_1+x)}{\sqrt{{\tan }^2(c_1+x)+1}}\}\}$$

Maple: cpu = 0.514 (sec), leaf count = 68 $$\{y\left(x\right)=a,y\left(x\right)=\tan (-x+\mathit{\_}\mathit{C}\mathit{1})\sqrt{\frac{a^2}{{(\tan (-x+\mathit{\_}\mathit{C}\mathit{1}))}^2+1}},y\left(x\right)=-a,y\left(x\right)=-\tan (-x+\mathit{\_}\mathit{C}\mathit{1})\sqrt{\frac{a^2}{{(\tan (-x+\mathit{\_}\mathit{C}\mathit{1}))}^2+1}}\}$$