\[ y'(x)=\frac {x^6-3 x^5+3 x^4 y(x)+4 x^4-6 x^3 y(x)-3 x^3+3 x^2 y(x)^2+5 x^2 y(x)-x^2-3 x y(x)^2-2 x y(x)+y(x)^3+y(x)^2+x+1}{x} \] ✓ Mathematica : cpu = 0.23742 (sec), leaf count = 108
DSolve[Derivative[1][y][x] == (1 + x - x^2 - 3*x^3 + 4*x^4 - 3*x^5 + x^6 - 2*x*y[x] + 5*x^2*y[x] - 6*x^3*y[x] + 3*x^4*y[x] + y[x]^2 - 3*x*y[x]^2 + 3*x^2*y[x]^2 + y[x]^3)/x,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 x^2-3 x+1}{x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.034 (sec), leaf count = 39
dsolve(diff(y(x),x) = (-x^2+x+1+y(x)^2+5*x^2*y(x)-2*x*y(x)+4*x^4-3*x^3+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))
\[y \left (x \right ) = -x^{2}+x -\frac {1}{3}+\frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x \right )+3 c_{1}\right )}{9}\]