\[ y'(x)=\frac {-x^6+3 x^4 y(x)^2+x^4-3 x^2 y(x)^4-2 x^2 y(x)^2+y(x)^6+y(x)^4+x+1}{y(x)} \] ✓ Mathematica : cpu = 0.27372 (sec), leaf count = 106
DSolve[Derivative[1][y][x] == (1 + x + x^4 - x^6 - 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],y[x],x]
\[\text {Solve}\left [\frac {1}{2} \text {RootSum}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^2-3 \text {$\#$1} y(x)^4-2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1} y(x)^2-2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\& \right ]-x=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.48 (sec), leaf count = 63
dsolve(diff(y(x),x) = (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(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}}{-\textit {\_a}^{6}+3 \textit {\_a}^{4} x^{2}-3 \textit {\_a}^{2} x^{4}+x^{6}-\textit {\_a}^{4}+2 \textit {\_a}^{2} x^{2}-x^{4}-1}d \textit {\_a} +x -c_{1} = 0\]