\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x}{-y \left ( x \right ) +1+ \left ( y \left ( x \right ) \right ) ^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{4}+ \left ( y \left ( x \right ) \right ) ^{6}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+3\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{6}}}=0} \]
Mathematica: cpu = 0.140518 (sec), leaf count = 103 \[ \text {Solve}\left [y(x)-\frac {1}{2} \text {RootSum}\left [\text {$\#$1}^3+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^2+3 \text {$\#$1} y(x)^4+2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2+6 \text {$\#$1} y(x)^2+2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ]=c_1,y(x)\right ] \]
Maple: cpu = 0.686 (sec), leaf count = 34 \[ \left \{ -y \left ( x \right ) +{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{ 2}+1 \right ) ^{-1}{d{\it \_a}}}{2}}-{\it \_C1}=0 \right \} \]