\[ y'(x)=\frac {x (x-y(x))^3 (y(x)+x)^3}{y(x) \left (x^2-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.17209 (sec), leaf count = 72
\[\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3-\text {$\#$1}+1\& ,\frac {\text {$\#$1} \log \left (-\text {$\#$1}+x^2-y(x)^2\right )-\log \left (-\text {$\#$1}+x^2-y(x)^2\right )}{3 \text {$\#$1}^2-1}\& \right ]+x^2=2 c_1,y(x)\right ]\]
✓ Maple : cpu = 0.925 (sec), leaf count = 190
\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac { \left ( {\it \_a}-y \left ( x \right ) \right ) ^{3} \left ( y \left ( x \right ) +{\it \_a} \right ) ^{3}{\it \_a}}{{{\it \_a}}^{6}-3\,{{\it \_a}}^{4} \left ( y \left ( x \right ) \right ) ^{2}+3\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{4}- \left ( y \left ( x \right ) \right ) ^{6}-{{\it \_a}}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{\frac { \left ( -{{\it \_f}}^{2}+{x}^{2}-1 \right ) {\it \_f}}{-{{\it \_f}}^{6}+3\,{{\it \_f}}^{4}{x}^{2}-3\,{{\it \_f}}^{2}{x}^{4}+{x}^{6}+{{\it \_f}}^{2}-{x}^{2}+1}}-\int _{{\it \_b}}^{x}\!4\,{\frac {{\it \_a}\, \left ( {\it \_f}+{\it \_a} \right ) ^{2} \left ( {{\it \_a}}^{2}-{{\it \_f}}^{2}-3/2 \right ) {\it \_f}\, \left ( {\it \_a}-{\it \_f} \right ) ^{2}}{ \left ( {{\it \_a}}^{6}-3\,{{\it \_a}}^{4}{{\it \_f}}^{2}+ \left ( 3\,{{\it \_f}}^{4}-1 \right ) {{\it \_a}}^{2}-{{\it \_f}}^{6}+{{\it \_f}}^{2}+1 \right ) ^{2}}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]