\[ \left (x^2+1\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2-1=0 \] ✓ Mathematica : cpu = 0.324827 (sec), leaf count = 95
\[\left \{\left \{y(x)\to \frac {-x+x \cosh (2 c_1)+x \sinh (2 c_1)-2 \cosh (c_1)-2 \sinh (c_1)}{1+\cosh (2 c_1)+\sinh (2 c_1)}\right \},\left \{y(x)\to \frac {-x+x \cosh (2 c_1)+x \sinh (2 c_1)+2 \cosh (c_1)+2 \sinh (c_1)}{1+\cosh (2 c_1)+\sinh (2 c_1)}\right \}\right \}\] ✓ Maple : cpu = 0.038 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+1},y \left ( x \right ) =-\sqrt {{x}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x-\sqrt {-{{\it \_C1}}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x+\sqrt {-{{\it \_C1}}^{2}+1} \right \} \]