\[ y'(x)=e^{2 x/3} \left (e^{-2 x} y(x)^3+e^{-4 x/3} y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.322516 (sec), leaf count = 114
DSolve[Derivative[1][y][x] == E^((2*x)/3)*(1 + y[x]^2/E^((4*x)/3) + y[x]^3/E^(2*x)),y[x],x]
\[\text {Solve}\left [-\frac {35}{3} \text {RootSum}\left [-35 \text {$\#$1}^3+9 \sqrt [3]{35} \text {$\#$1}-35\& ,\frac {\log \left (\frac {3 e^{-4 x/3} y(x)+e^{-2 x/3}}{\sqrt [3]{35} \sqrt [3]{e^{-2 x}}}-\text {$\#$1}\right )}{3 \sqrt [3]{35}-35 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 35^{2/3} e^{4 x/3} \left (e^{-2 x}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.114 (sec), leaf count = 40
dsolve(diff(y(x),x) = (1+y(x)^2*exp(-4/3*x)+y(x)^3*exp(-2*x))*exp(2/3*x),y(x))
\[y \left (x \right ) = \RootOf \left (-x +3 \left (\int _{}^{\textit {\_Z}}\frac {1}{3 \textit {\_a}^{3}+3 \textit {\_a}^{2}-2 \textit {\_a} +3}d \textit {\_a} \right )+c_{1}\right ) {\mathrm e}^{\frac {2 x}{3}}\]