\[ y'(x)=\frac {3 x^4 y(x)^2-3 x^2 y(x)^4-2 x^2 y(x)^2-x^6+x^4+y(x)^6+y(x)^4+x+1}{y(x)} \] ✓ Mathematica : cpu = 0.274243 (sec), leaf count = 106
\[\text {Solve}\left [\frac {1}{2} \text {RootSum}\left [3 \text {$\#$1}^2 y(x)^2-\text {$\#$1}^3+\text {$\#$1}^2-3 \text {$\#$1} y(x)^4-2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1} y(x)^2-2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ]-x=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.795 (sec), leaf count = 63
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {{\it \_a}}{-{{\it \_a}}^{6}+3\,{{\it \_a}}^{4}{x}^{2}-3\,{x}^{4}{{\it \_a}}^{2}+{x}^{6}-{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{x}^{2}-{x}^{4}-1}}\,{\rm d}{\it \_a}+x-{\it \_C1}=0 \right \} \]