\[ y'(x)=\frac {x}{3 x^4 y(x)^2+3 x^2 y(x)^4+2 x^2 y(x)^2+x^6+x^4+y(x)^6+y(x)^4-y(x)+1} \] ✓ Mathematica : cpu = 0.171611 (sec), leaf count = 103
\[\text {Solve}\left [y(x)-\frac {1}{2} \text {RootSum}\left [3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^3+\text {$\#$1}^2+3 \text {$\#$1} y(x)^4+2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2+6 \text {$\#$1} y(x)^2+2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.9 (sec), leaf count = 34
\[ \left \{ -y \left ( x \right ) +{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}}{2}}-{\it \_C1}=0 \right \} \]