3.446   ODE No. 446

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

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

Mathematica: cpu = 0.490562 (sec), leaf count = 201 $$\{\{y(x)\to \frac{e^{2c_1}x-2e^{c_1}-x}{e^{2c_1}+1}\},\{y(x)\to \frac{e^{2c_1}x+2e^{c_1}-x}{e^{2c_1}+1}\},\{y(x)\to \frac{-e^{4c_1}x-2\sqrt{-e^{2c_1}+2e^{4c_1}-e^{6c_1}}+x}{2e^{2c_1}-e^{4c_1}-1}\},\{y(x)\to \frac{-e^{4c_1}x+2\sqrt{-e^{2c_1}+2e^{4c_1}-e^{6c_1}}+x}{2e^{2c_1}-e^{4c_1}-1}\}\}$$

Maple: cpu = 0.577 (sec), leaf count = 57 $$\{y\left(x\right)=\sqrt{x^2+1},y\left(x\right)=-\sqrt{x^2+1},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x-\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2+1},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2+1}\}$$