\[ y'(x)=\frac {x^6}{27}+\frac {1}{3} x^4 y(x)+\frac {x^4}{9}+x^2 y(x)^2+\frac {2}{3} x^2 y(x)+y(x)^3+y(x)^2-\frac {2 x}{3}+1 \] ✓ Mathematica : cpu = 0.202909 (sec), leaf count = 77
DSolve[Derivative[1][y][x] == 1 - (2*x)/3 + x^4/9 + x^6/27 + (2*x^2*y[x])/3 + (x^4*y[x])/3 + y[x]^2 + x^2*y[x]^2 + y[x]^3,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {x^2+3 y(x)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.06 (sec), leaf count = 30
dsolve(diff(y(x),x) = -2/3*x+1+y(x)^2+2/3*x^2*y(x)+1/9*x^4+y(x)^3+x^2*y(x)^2+1/3*y(x)*x^4+1/27*x^6,y(x))
\[y \left (x \right ) = -\frac {x^{2}}{3}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} +c_{1}\right )\]