\[ y'(x)=e^x \left (e^{-3 x} y(x)^3+e^{-2 x} y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.252682 (sec), leaf count = 108
\[\text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {3 e^{-2 x} y(x)+e^{-x}}{\sqrt [3]{38} \sqrt [3]{e^{-3 x}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 38^{2/3} e^{2 x} \left (e^{-3 x}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.265 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}-{\it \_a}+1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{{\rm e}^{-x}}}} \right \} \]