\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( x-y \left ( x \right ) \right ) ^{3} \left ( y \left ( x \right ) +x \right ) ^{3}x}{ \left ( - \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}-1 \right ) y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.141018 (sec), leaf count = 74 \[ \text {Solve}\left [\frac {1}{2} \left (\text {RootSum}\left [\text {$\#$1}^3-\text {$\#$1}+1\& ,\frac {\text {$\#$1} \log \left (-\text {$\#$1}+x^2-y(x)^2\right )-\log \left (-\text {$\#$1}+x^2-y(x)^2\right )}{3 \text {$\#$1}^2-1}\& \right ]+x^2\right )=c_1,y(x)\right ] \]
Maple: cpu = 0.624 (sec), leaf count = 307 \[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( {\it \_a}-y \left ( x \right ) \right ) ^{3} \left ( y \left ( x \right ) +{\it \_a} \right ) ^{ 3}{\it \_a}}{{{\it \_a}}^{6}-3\,{{\it \_a}}^{4} \left ( y \left ( x \right ) \right ) ^{2}+3\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{4}- \left ( y \left ( x \right ) \right ) ^{6}-{{\it \_a}}^{2} + \left ( y \left ( x \right ) \right ) ^{2}+1}}\,{\rm d}{\it \_a}+\int ^ {y \left ( x \right ) }\!-{\frac { \left ( -{{\it \_f}}^{2}+{x}^{2}-1 \right ) {\it \_f}}{-{{\it \_f}}^{6}+3\,{{\it \_f}}^{4}{x}^{2}-3\,{{ \it \_f}}^{2}{x}^{4}+{x}^{6}+{{\it \_f}}^{2}-{x}^{2}+1}}-\int _{{\it \_b}}^{x}\!-{\frac { \left ( {\it \_a}-{\it \_f} \right ) ^{3} \left ( { \it \_f}+{\it \_a} \right ) ^{3}{\it \_a}\, \left ( -6\,{{\it \_a}}^{4}{ \it \_f}+12\,{{\it \_a}}^{2}{{\it \_f}}^{3}-6\,{{\it \_f}}^{5}+2\,{ \it \_f} \right ) }{ \left ( {{\it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f }}^{2}+3\,{{\it \_a}}^{2}{{\it \_f}}^{4}-{{\it \_f}}^{6}-{{\it \_a}}^{ 2}+{{\it \_f}}^{2}+1 \right ) ^{2}}}-3\,{\frac { \left ( {\it \_a}-{\it \_f} \right ) ^{2} \left ( {\it \_f}+{\it \_a} \right ) ^{3}{\it \_a}}{{{ \it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f}}^{2}+3\,{{\it \_a}}^{2}{{ \it \_f}}^{4}-{{\it \_f}}^{6}-{{\it \_a}}^{2}+{{\it \_f}}^{2}+1}}+3\,{ \frac { \left ( {\it \_a}-{\it \_f} \right ) ^{3} \left ( {\it \_f}+{\it \_a} \right ) ^{2}{\it \_a}}{{{\it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f}}^{2}+3\,{{\it \_a}}^{2}{{\it \_f}}^{4}-{{\it \_f}}^{6}-{{\it \_a} }^{2}+{{\it \_f}}^{2}+1}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]