\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x+1+ \left ( y \left ( x \right ) \right ) ^{4}-2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{4}+ \left ( y \left ( x \right ) \right ) ^{6}-3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+3\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}-{x}^{6}}{y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.201026 (sec), leaf count = 106 \[ \text {Solve}\left [\frac {1}{2} \text {RootSum}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^2-3 \text {$\#$1} y(x)^4-2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1} y(x)^2-2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ]-x=c_1,y(x)\right ] \]
Maple: cpu = 0.296 (sec), leaf count = 63 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {{\it \_a}}{-{ {\it \_a}}^{6}+3\,{{\it \_a}}^{4}{x}^{2}-3\,{{\it \_a}}^{2}{x}^{4}+{x} ^{6}-{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{x}^{2}-{x}^{4}-1}}\,{\rm d}{ \it \_a}+x-{\it \_C1}=0 \right \} \]