\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{3}{{\rm e}^{-4/3\,x}}}{y \left ( x \right ) {{\rm e}^{-2/3\,x}}+1}}=0} \]
Mathematica: cpu = 11.358942 (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 = 0.920 (sec), leaf count = 64 \[ \left \{ x+{\frac {3}{2}\ln \left ( y \left ( x \right ) {{\rm e}^{-{ \frac {2\,x}{3}}}} \right ) }-{\frac {3}{4}\ln \left ( 3\, \left ( y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{-2/3\,x}} \right ) ^{2 }-2\,y \left ( x \right ) {{\rm e}^{-2/3\,x}}-2 \right ) }+{\frac {3\, \sqrt {7}}{14}{\it Artanh} \left ( {\frac {\sqrt {7}}{14} \left ( 6\,y \left ( x \right ) {{\rm e}^{-2/3\,x}}-2 \right ) } \right ) }-{\it \_C1} =0 \right \} \]