\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) = \left ( 1+ \left ( y \left ( x \right ) \right ) ^{2}{{\rm e}^{-2\,x}}+ \left ( y \left ( x \right ) \right ) ^{3}{{\rm e}^{-3\,x}} \right ) {{\rm e}^{x}}=0} \]
Mathematica: cpu = 0.132517 (sec), leaf count = 108 \[ \text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {3 e^{-2 x} y(x)+e^{-x}}{\sqrt [3]{38} \sqrt [3]{e^{-3 x}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 38^{2/3} e^{2 x} \left (e^{-3 x}\right )^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 34 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -x+\int ^{{ \it \_Z}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}-{\it \_a}+1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{{\rm e}^{-x}}}} \right \} \]