\[ y'(x)=\frac {x (x-y(x))^3 (y(x)+x)^3}{y(x) \left (x^2-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.16294 (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 = 36.955 (sec), leaf count = 307
\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( {\it \_a}-y \left ( x \right ) \right ) ^{3} \left ( y \left ( x \right ) +{\it \_a} \right ) ^{3}{\it \_a}}{{{\it \_a}}^{6}-3\,{{\it \_a}}^{4} \left ( y \left ( x \right ) \right ) ^{2}+3\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{4}- \left ( y \left ( x \right ) \right ) ^{6}-{{\it \_a}}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{\frac { \left ( -{{\it \_f}}^{2}+{x}^{2}-1 \right ) {\it \_f}}{-{{\it \_f}}^{6}+3\,{{\it \_f}}^{4}{x}^{2}-3\,{{\it \_f}}^{2}{x}^{4}+{x}^{6}+{{\it \_f}}^{2}-{x}^{2}+1}}-\int _{{\it \_b}}^{x}\!-{\frac { \left ( {\it \_a}-{\it \_f} \right ) ^{3} \left ( {\it \_a}+{\it \_f} \right ) ^{3}{\it \_a}\, \left ( -6\,{{\it \_a}}^{4}{\it \_f}+12\,{{\it \_a}}^{2}{{\it \_f}}^{3}-6\,{{\it \_f}}^{5}+2\,{\it \_f} \right ) }{ \left ( {{\it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f}}^{2}+3\,{{\it \_a}}^{2}{{\it \_f}}^{4}-{{\it \_f}}^{6}-{{\it \_a}}^{2}+{{\it \_f}}^{2}+1 \right ) ^{2}}}-3\,{\frac { \left ( {\it \_a}-{\it \_f} \right ) ^{2} \left ( {\it \_a}+{\it \_f} \right ) ^{3}{\it \_a}}{{{\it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f}}^{2}+3\,{{\it \_a}}^{2}{{\it \_f}}^{4}-{{\it \_f}}^{6}-{{\it \_a}}^{2}+{{\it \_f}}^{2}+1}}+3\,{\frac { \left ( {\it \_a}-{\it \_f} \right ) ^{3} \left ( {\it \_a}+{\it \_f} \right ) ^{2}{\it \_a}}{{{\it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f}}^{2}+3\,{{\it \_a}}^{2}{{\it \_f}}^{4}-{{\it \_f}}^{6}-{{\it \_a}}^{2}+{{\it \_f}}^{2}+1}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]