3.448   ODE No. 448

$$\boxed{{\displaystyle (x^2-1){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-{\left(y\left(x\right)\right)}^2+1=0}}$$

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

Mathematica: cpu = 0.091512 (sec), leaf count = 109 $$\{\{y(x)\to \frac{1}{2}(e^{-c_1}\sqrt{x^2-1}-e^{c_1}\sqrt{x^2-1}+e^{-c_1}x+e^{c_1}x)\},\{y(x)\to \frac{1}{2}(-e^{-c_1}\sqrt{x^2-1}+e^{c_1}\sqrt{x^2-1}+e^{-c_1}x+e^{c_1}x)\}\}$$

Maple: cpu = 10.858 (sec), leaf count = 166 $$\{1\sqrt{(-1+y\left(x\right))(1+y\left(x\right))}\ln (y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-1})\frac{1}{\sqrt{-1+y\left(x\right)}}\frac{1}{\sqrt{1+y\left(x\right)}}+{\int }^x\frac{1}{{\mathit{\_}\mathit{a}}^2-1}\sqrt{({\mathit{\_}\mathit{a}}^2-1)({\left(y\left(x\right)\right)}^2-1)}\frac{1}{\sqrt{-1+y\left(x\right)}}\frac{1}{\sqrt{1+y\left(x\right)}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0,1\sqrt{(-1+y\left(x\right))(1+y\left(x\right))}\ln (y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-1})\frac{1}{\sqrt{-1+y\left(x\right)}}\frac{1}{\sqrt{1+y\left(x\right)}}+{\int }^x-\frac{1}{{\mathit{\_}\mathit{a}}^2-1}\sqrt{({\mathit{\_}\mathit{a}}^2-1)({\left(y\left(x\right)\right)}^2-1)}\frac{1}{\sqrt{-1+y\left(x\right)}}\frac{1}{\sqrt{1+y\left(x\right)}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=-1,y\left(x\right)=1\}$$