\[ y'(x)=\frac {x^6}{27}+\frac {1}{3} x^4 y(x)+\frac {x^4}{9}+x^2 y(x)^2+\frac {2}{3} x^2 y(x)+y(x)^3+y(x)^2-\frac {2 x}{3}+1 \] ✓ Mathematica : cpu = 0.0818474 (sec), leaf count = 75
\[\text {Solve}\left [87 \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {x^2+3 y(x)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]+9 c_1+29^{2/3} x=0,y(x)\right ]\]
✓ Maple : cpu = 0.07 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{3}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]