\[ \boxed { \left ( {x}^{2}+1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,xy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}-1=0} \]
Mathematica: cpu = 0.490562 (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 = 0.577 (sec), leaf count = 57 \[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+1},y \left ( x \right ) =- \sqrt {{x}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x-\sqrt {-{{\it \_C1 }}^{2}+1},y \left ( x \right ) ={\it \_C1}\,x+\sqrt {-{{\it \_C1}}^{2}+1 } \right \} \]