\[ \left (x^2+1\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2-1=0 \] ✓ Mathematica : cpu = 0.506068 (sec), leaf count = 201
\[\left \{\left \{y(x)\to \frac {e^{2 c_1} x-2 e^{c_1}-x}{e^{2 c_1}+1}\right \},\left \{y(x)\to \frac {e^{2 c_1} x+2 e^{c_1}-x}{e^{2 c_1}+1}\right \},\left \{y(x)\to \frac {-e^{4 c_1} x-2 \sqrt {-e^{2 c_1}+2 e^{4 c_1}-e^{6 c_1}}+x}{2 e^{2 c_1}-e^{4 c_1}-1}\right \},\left \{y(x)\to \frac {-e^{4 c_1} x+2 \sqrt {-e^{2 c_1}+2 e^{4 c_1}-e^{6 c_1}}+x}{2 e^{2 c_1}-e^{4 c_1}-1}\right \}\right \}\] ✓ Maple : cpu = 0.385 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+1},y \left ( x \right ) =-\sqrt {{x}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x-\sqrt {-{{\it \_C1}}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x+\sqrt {-{{\it \_C1}}^{2}+1} \right \} \]