\[ -\frac {1}{x^5}+\left (2 x+e^x\right ) y^{(4)}(x)+4 \left (e^x+2\right ) y^{(3)}(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0 \] ✓ Mathematica : cpu = 0.133231 (sec), leaf count = 77
\[\left \{\left \{y(x)\to \frac {c_4 x^3}{2 x+e^x}+\frac {c_3 x^2}{2 x+e^x}+\frac {1}{24 \left (2 x+e^x\right ) x}+\frac {c_2 x}{2 x+e^x}+\frac {c_1}{2 x+e^x}\right \}\right \}\] ✓ Maple : cpu = 0.038 (sec), leaf count = 41
\[y \relax (x ) = \frac {24 x^{4} c_{1}+24 x^{3} c_{2}+24 x^{2} c_{3}+24 x c_{4}+1}{24 \left ({\mathrm e}^{x}+2 x \right ) x}\]