3.492   ODE No. 492

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

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

Mathematica: cpu = 0.282536 (sec), leaf count = 111 $$\{\{y(x)\to \text{InverseFunction}[\sqrt{a^2-{\mathrm{\#}\text{1}}^2}-a\log (a\sqrt{a^2-{\mathrm{\#}\text{1}}^2}+a^2)+a\log (\mathrm{\#}\text{1})\mathrm{\&}][c_1-x]\},\{y(x)\to \text{InverseFunction}[\sqrt{a^2-{\mathrm{\#}\text{1}}^2}-a\log (a\sqrt{a^2-{\mathrm{\#}\text{1}}^2}+a^2)+a\log (\mathrm{\#}\text{1})\mathrm{\&}][c_1+x]\}\}$$

Maple: cpu = 0.905 (sec), leaf count = 122 $$\{x-\sqrt{a^2-{\left(y\left(x\right)\right)}^2}+a^2\ln \left(\frac{1}{y\left(x\right)}(2a^2+2\sqrt{a^2}\sqrt{a^2-{\left(y\left(x\right)\right)}^2})\right)\frac{1}{\sqrt{a^2}}-\mathit{\_}\mathit{C}\mathit{1}=0,x+\sqrt{a^2-{\left(y\left(x\right)\right)}^2}-a^2\ln \left(\frac{1}{y\left(x\right)}(2a^2+2\sqrt{a^2}\sqrt{a^2-{\left(y\left(x\right)\right)}^2})\right)\frac{1}{\sqrt{a^2}}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$