\[ -\frac {1}{x^5}+\left (2 x+e^x\right ) y^{(4)}(x)+4 \left (e^x+2\right ) y^{(3)}(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0 \] ✓ Mathematica : cpu = 0.173271 (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 = 0.056 (sec), leaf count = 41
\[\left \{y \left (x \right ) = \frac {24 c_{1} x^{4}+24 c_{2} x^{3}+24 c_{3} x^{2}+24 c_{4} x +1}{24 \left (2 x +{\mathrm e}^{x}\right ) x}\right \}\]