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 = 0.0597772 (sec), leaf count = 139

$$\{\{y(x)\to c_1-\frac{ix\sqrt{x^2-a^2}\log \left(\frac{2(\sqrt{x^2-a^2}-ia)}{x}\right)}{a\sqrt{x^4-a^2{x}^2}}\},\{y(x)\to c_1+\frac{ix\sqrt{x^2-a^2}\log \left(\frac{2(\sqrt{x^2-a^2}-ia)}{x}\right)}{a\sqrt{x^4-a^2{x}^2}}\}\}$$

✓ Maple : cpu = 0.046 (sec), leaf count = 90

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