2.446   ODE No. 446

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

$$(x^2+1)y^{\prime }(x{)}^2-2xy(x)y^{\prime }(x)+y(x{)}^2-1=0$$ ✓ Mathematica : cpu = 0.324827 (sec), leaf count = 95

$$\{\{y(x)\to \frac{-x+x\cosh (2c_1)+x\sinh (2c_1)-2\cosh (c_1)-2\sinh (c_1)}{1+\cosh (2c_1)+\sinh (2c_1)}\},\{y(x)\to \frac{-x+x\cosh (2c_1)+x\sinh (2c_1)+2\cosh (c_1)+2\sinh (c_1)}{1+\cosh (2c_1)+\sinh (2c_1)}\}\}$$ ✓ Maple : cpu = 0.038 (sec), leaf count = 57

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