2.448   ODE No. 448

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

$$(x^2-1)y^{\prime }(x{)}^2-y(x{)}^2+1=0$$ ✓ Mathematica : cpu = 0.0925097 (sec), leaf count = 349

$$\{\{y(x)\to -\frac{1}{2}{e}^{-c_1}\sqrt{2x^2+2e^{4c_1}{x}^2-2\sqrt{(x-1)(x+1)}x+2e^{4c_1}\sqrt{(x-1)(x+1)}x-1+2e^{2c_1}-e^{4c_1}}\},\{y(x)\to \frac{1}{2}{e}^{-c_1}\sqrt{2x^2+2e^{4c_1}{x}^2-2\sqrt{(x-1)(x+1)}x+2e^{4c_1}\sqrt{(x-1)(x+1)}x-1+2e^{2c_1}-e^{4c_1}}\},\{y(x)\to -\frac{1}{2}\sqrt{2e^{-2c_1}{x}^2+2e^{2c_1}{x}^2+2e^{-2c_1}\sqrt{x^2-1}x-2e^{2c_1}\sqrt{x^2-1}x+2-e^{-2c_1}-e^{2c_1}}\},\{y(x)\to \frac{1}{2}\sqrt{2e^{-2c_1}{x}^2+2e^{2c_1}{x}^2+2e^{-2c_1}\sqrt{x^2-1}x-2e^{2c_1}\sqrt{x^2-1}x+2-e^{-2c_1}-e^{2c_1}}\}\}$$ ✗ Maple : cpu = 0. (sec), leaf count = 0 , exception

time expired