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 = 0.0230423 (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 = 0.061 (sec), leaf count = 90

$$\{y\left(x\right)=c_1-\frac{\ln \left(\frac{-2a^2+2\sqrt{-a^2}\sqrt{-a^2+x^2}}{x}\right)}{\sqrt{-a^2}},y\left(x\right)=c_1+\frac{\ln \left(\frac{-2a^2+2\sqrt{-a^2}\sqrt{-a^2+x^2}}{x}\right)}{\sqrt{-a^2}}\}$$