\[ \left (x^2+1\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2-1=0 \] ✓ Mathematica : cpu = 0.568138 (sec), leaf count = 167
\[\left \{\left \{y(x)\to -\frac {-e^{2 c_1} x+2 e^{c_1}+x}{e^{2 c_1}+1}\right \},\left \{y(x)\to \frac {e^{2 c_1} x+2 e^{c_1}-x}{e^{2 c_1}+1}\right \},\left \{y(x)\to \frac {\left (e^{4 c_1}-1\right ) x+2 \sqrt {-e^{2 c_1} \left (e^{2 c_1}-1\right ){}^2}}{\left (e^{2 c_1}-1\right ){}^2}\right \},\left \{y(x)\to \frac {\left (e^{4 c_1}-1\right ) x-2 \sqrt {-e^{2 c_1} \left (e^{2 c_1}-1\right ){}^2}}{\left (e^{2 c_1}-1\right ){}^2}\right \}\right \}\]
✓ Maple : cpu = 0.134 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+1},y \left ( x \right ) =-\sqrt {{x}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x-\sqrt {-{{\it \_C1}}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x+\sqrt {-{{\it \_C1}}^{2}+1} \right \} \]