3.209   ODE No. 209

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

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

Mathematica: cpu = 0.021003 (sec), leaf count = 84 $$\{\{y(x)\to -\frac{\sqrt{2a^2{c}_{1}x+a^2{c}_1^2+a^2{x}^2-b}}{\sqrt{a}}\},\{y(x)\to \frac{\sqrt{2a^2{c}_{1}x+a^2{c}_1^2+a^2{x}^2-b}}{\sqrt{a}}\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 21 $$\{x-\frac{1}{a}\sqrt{a{\left(y\left(x\right)\right)}^2+b}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$