\[ y'(x)=\frac {e^{-4 x/3} y(x)^3}{e^{-2 x/3} y(x)+1} \] ✓ Mathematica : cpu = 15.3076 (sec), leaf count = 82
\[\text {Solve}\left [\frac {3}{2} \log (y(x))+\frac {1}{28} \left (-21 \log \left (-3 y(x)^2+2 e^{2 x/3} y(x)+2 e^{4 x/3}\right )+6 \sqrt {7} \tanh ^{-1}\left (\frac {y(x)+2 e^{2 x/3}}{\sqrt {7} y(x)}\right )+28 x\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 2.632 (sec), leaf count = 66
\[ \left \{ x+{\frac {3\,\sqrt {7}}{14}{\it Artanh} \left ( {\frac {3\,y \left ( x \right ) \sqrt {7}}{7}{{\rm e}^{-{\frac {2\,x}{3}}}}}-{\frac {\sqrt {7}}{7}} \right ) }-{\frac {3}{4}\ln \left ( 3\, \left ( y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{-2/3\,x}} \right ) ^{2}-2\,y \left ( x \right ) {{\rm e}^{-2/3\,x}}-2 \right ) }+{\frac {3}{2}\ln \left ( y \left ( x \right ) {{\rm e}^{-{\frac {2\,x}{3}}}} \right ) }-{\it \_C1}=0 \right \} \]