2.458   ODE No. 458

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

$$x^2(x^2-a^2)y^{\prime }(x{)}^2-1=0$$ ✓ Mathematica : cpu = 0.0205922 (sec), leaf count = 120

$$\{\{y(x)\to -\frac{x\sqrt{x^2-a^2}{\tan }^{-1}\left(\frac{\sqrt{x^2-a^2}}{a}\right)}{a\sqrt{x^4-a^2{x}^2}}+c_1\},\{y(x)\to \frac{x\sqrt{x^2-a^2}{\tan }^{-1}\left(\frac{\sqrt{x^2-a^2}}{a}\right)}{a\sqrt{x^4-a^2{x}^2}}+c_1\}\}$$ ✓ Maple : cpu = 0.154 (sec), leaf count = 90

$$\{y\left(x\right)=-\ln \left(\frac{1}{x}(-2a^2+2\sqrt{-a^2}\sqrt{-a^2+x^2})\right)\frac{1}{\sqrt{-a^2}}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\ln \left(\frac{1}{x}(-2a^2+2\sqrt{-a^2}\sqrt{-a^2+x^2})\right)\frac{1}{\sqrt{-a^2}}+\mathit{\_}\mathit{C}\mathit{1}\}$$