\[ y'(x)=\frac {x}{x^6+3 x^4 y(x)^2+x^4+3 x^2 y(x)^4+2 x^2 y(x)^2+y(x)^6+y(x)^4-y(x)+1} \] ✓ Mathematica : cpu = 0.192657 (sec), leaf count = 103
DSolve[Derivative[1][y][x] == x/(1 + x^4 + x^6 - y[x] + 2*x^2*y[x]^2 + 3*x^4*y[x]^2 + y[x]^4 + 3*x^2*y[x]^4 + y[x]^6),y[x],x]
\[\text {Solve}\left [y(x)-\frac {1}{2} \text {RootSum}\left [\text {$\#$1}^3+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^2+3 \text {$\#$1} y(x)^4+2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2+6 \text {$\#$1} y(x)^2+2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.633 (sec), leaf count = 34
dsolve(diff(y(x),x) = x/(-y(x)+1+y(x)^4+2*x^2*y(x)^2+x^4+y(x)^6+3*x^2*y(x)^4+3*x^4*y(x)^2+x^6),y(x))
\[-y \left (x \right )+\frac {\left (\int _{}^{y \left (x \right )^{2}+x^{2}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )}{2}-c_{1} = 0\]