\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) = \left ( 1+ \left ( y \left ( x \right ) \right ) ^{2}{{\rm e}^{-4/3\,x}}+ \left ( y \left ( x \right ) \right ) ^{3}{{\rm e}^{-2\,x}} \right ) {{\rm e}^{2/3\,x}}=0} \]
Mathematica: cpu = 0.129016 (sec), leaf count = 114 \[ \text {Solve}\left [-\frac {35}{3} \text {RootSum}\left [-35 \text {$\#$1}^3+9 \sqrt [3]{35} \text {$\#$1}-35\& ,\frac {\log \left (\frac {3 e^{-4 x/3} y(x)+e^{-2 x/3}}{\sqrt [3]{35} \sqrt [3]{e^{-2 x}}}-\text {$\#$1}\right )}{3 \sqrt [3]{35}-35 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 35^{2/3} e^{4 x/3} \left (e^{-2 x}\right )^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.078 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={{\it RootOf} \left ( -x+3\,\int ^{{\it \_Z}}\! \left ( 3\,{{\it \_a}}^{3}+3\,{{\it \_a}}^{2}-2\,{\it \_a}+3 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \left ( {{\rm e}^{-{ \frac {2\,x}{3}}}} \right ) ^{-1}} \right \} \]