\[ y'(x)=e^x \left (e^{-3 x} y(x)^3+e^{-2 x} y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.31447 (sec), leaf count = 108
DSolve[Derivative[1][y][x] == E^x*(1 + y[x]^2/E^(2*x) + y[x]^3/E^(3*x)),y[x],x]
\[\text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {3 e^{-2 x} y(x)+e^{-x}}{\sqrt [3]{38} \sqrt [3]{e^{-3 x}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 38^{2/3} e^{2 x} \left (e^{-3 x}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.099 (sec), leaf count = 34
dsolve(diff(y(x),x) = (1+y(x)^2*exp(-2*x)+y(x)^3*exp(-3*x))*exp(x),y(x))
\[y \left (x \right ) = \RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}-\textit {\_a} +1}d \textit {\_a} +c_{1}\right ) {\mathrm e}^{x}\]