\[ y'(x)=\frac {x^6-3 x^5+3 x^4 y(x)+x^4-6 x^3 y(x)+2 x^3+3 x^2 y(x)^2+x^2 y(x)-3 x^2-3 x y(x)^2+x y(x)+y(x)^3+x}{x \left (x^2+y(x)-x+1\right )} \] ✓ Mathematica : cpu = 0.202494 (sec), leaf count = 76
DSolve[Derivative[1][y][x] == (x - 3*x^2 + 2*x^3 + x^4 - 3*x^5 + x^6 + x*y[x] + x^2*y[x] - 6*x^3*y[x] + 3*x^4*y[x] - 3*x*y[x]^2 + 3*x^2*y[x]^2 + y[x]^3)/(x*(1 - x + x^2 + y[x])),y[x],x]
\[\left \{\left \{y(x)\to -x^2+x+\frac {1}{x \left (\frac {1}{x}-\frac {1}{x \sqrt {-2 \log (x)+c_1}}\right )}-1\right \},\left \{y(x)\to -x^2+x+\frac {1}{x \left (\frac {1}{x}+\frac {1}{x \sqrt {-2 \log (x)+c_1}}\right )}-1\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 81
dsolve(diff(y(x),x) = (x^2*y(x)+x^4+2*x^3-3*x^2+x*y(x)+x+y(x)^3+3*x^2*y(x)^2-3*x*y(x)^2+3*y(x)*x^4-6*x^3*y(x)+x^6-3*x^5)/x/(y(x)+x^2-x+1),y(x))
\[y \left (x \right ) = \frac {\left (-x^{2}+x \right ) \sqrt {c_{1}-2 \ln \left (x \right )}+x^{2}-x +1}{-1+\sqrt {c_{1}-2 \ln \left (x \right )}}\]