\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-2\,xy \left ( x \right ) +2\,{x}^{3}-2\,x- \left ( y \left ( x \right ) \right ) ^{3}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-3\,y \left ( x \right ) {x}^{4}+{x}^{6}}{-y \left ( x \right ) +{x}^{2}-1}}=0} \]
Mathematica: cpu = 0.016502 (sec), leaf count = 49 \[ \left \{\left \{y(x)\to \frac {1}{1-\frac {1}{\sqrt {c_1-2 x}}}+x^2-1\right \},\left \{y(x)\to \frac {1}{\frac {1}{\sqrt {c_1-2 x}}+1}+x^2-1\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 71 \[ \left \{ y \left ( x \right ) =-{\frac {1}{-2\,x+2\,{\it \_C1}} \left ( - 2\,{\it \_C1}\,{x}^{2}+2\,{x}^{3}+\sqrt {2\,{\it \_C1}-2\,x+1}-1 \right ) },y \left ( x \right ) ={\frac {1}{-2\,x+2\,{\it \_C1}} \left ( 2\,{\it \_C1}\,{x}^{2}-2\,{x}^{3}+\sqrt {2\,{\it \_C1}-2\,x+1}+1 \right ) } \right \} \]