\[ y'(x)=\frac {-x^6+3 x^4 y(x)^2+x^4-3 x^2 y(x)^4-2 x^2 y(x)^2+y(x)^6+y(x)^4+x+1}{y(x)} \] ✓ Mathematica : cpu = 0.258716 (sec), leaf count = 102
\[\text {Solve}\left [2 \left (c_1+x\right )=\text {RootSum}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^2-3 \text {$\#$1} y(x)^4-2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1} y(x)^2-2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ],y(x)\right ]\]
✓ Maple : cpu = 0.832 (sec), leaf count = 63
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {{\it \_a}}{-{{\it \_a}}^{6}+3\,{{\it \_a}}^{4}{x}^{2}-3\,{{\it \_a}}^{2}{x}^{4}+{x}^{6}-{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{x}^{2}-{x}^{4}-1}}\,{\rm d}{\it \_a}+x-{\it \_C1}=0 \right \} \]