\[ y'(x)=\frac {e^{-4 x/3} y(x)^3}{e^{-2 x/3} y(x)+1} \] ✓ Mathematica : cpu = 11.3154 (sec), leaf count = 82
DSolve[Derivative[1][y][x] == y[x]^3/(E^((4*x)/3)*(1 + y[x]/E^((2*x)/3))),y[x],x]
\[\text {Solve}\left [\frac {3}{2} \log (y(x))+\frac {1}{28} \left (-21 \log \left (-3 y(x)^2+2 e^{2 x/3} y(x)+2 e^{4 x/3}\right )+6 \sqrt {7} \tanh ^{-1}\left (\frac {y(x)+2 e^{2 x/3}}{\sqrt {7} y(x)}\right )+28 x\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.789 (sec), leaf count = 66
dsolve(diff(y(x),x) = y(x)^3/(y(x)*exp(-2/3*x)+1)*exp(-4/3*x),y(x))
\[x +\frac {3 \sqrt {7}\, \arctanh \left (\frac {3 y \left (x \right ) \sqrt {7}\, {\mathrm e}^{-\frac {2 x}{3}}}{7}-\frac {\sqrt {7}}{7}\right )}{14}-\frac {3 \ln \left (3 y \left (x \right )^{2} {\mathrm e}^{-\frac {4 x}{3}}-2 y \left (x \right ) {\mathrm e}^{-\frac {2 x}{3}}-2\right )}{4}+\frac {3 \ln \left (y \left (x \right ) {\mathrm e}^{-\frac {2 x}{3}}\right )}{2}-c_{1} = 0\]