\[ \boxed { x \left ( {x}^{2}-1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\, \left ( -{x}^{2}+1 \right ) y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( y \left ( x \right ) \right ) ^{2}-x=0} \]
Mathematica: cpu = 0.122516 (sec), leaf count = 79 \[ \left \{\left \{y(x)\to x+2 x \sinh ^2\left (\frac {1}{2} \left (c_1-2 i \tan ^{-1}\left (\frac {\sqrt {x-1}}{\sqrt {x+1}}\right )\right )\right )\right \},\left \{y(x)\to x+2 x \sinh ^2\left (\frac {1}{2} \left (c_1+2 i \tan ^{-1}\left (\frac {\sqrt {x-1}}{\sqrt {x+1}}\right )\right )\right )\right \}\right \} \]
Maple: cpu = 0.874 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) =x,y \left ( x \right ) =-x,y \left ( x \right ) =\sqrt {-{{\it \_C1}}^{2}+1}+\sqrt {{x}^{2}-1}{\it \_C1} \right \} \]