ODE
\[ 4 \left (e^x+2\right ) y'''(x)+\left (2 x+e^x\right ) y''''(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0 \] ODE Classification
[[_high_order, _fully, _exact, _linear]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.293907 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {x (x (c_4 x+c_3)+c_2)+c_1}{2 x+e^x}\right \}\right \}\]
Maple ✓
cpu = 0.227 (sec), leaf count = 52
\[\left [y \left (x \right ) = \frac {x^{2} \textit {\_C2}}{2 x +{\mathrm e}^{x}}+\frac {x^{3} \textit {\_C1}}{2 x +{\mathrm e}^{x}}+\frac {\textit {\_C3} x}{2 x +{\mathrm e}^{x}}+\frac {\textit {\_C4}}{2 x +{\mathrm e}^{x}}\right ]\] Mathematica raw input
DSolve[E^x*y[x] + 4*E^x*y'[x] + 6*E^x*y''[x] + 4*(2 + E^x)*y'''[x] + (E^x + 2*x)*y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*(C[2] + x*(C[3] + x*C[4])))/(E^x + 2*x)}}
Maple raw input
dsolve((2*x+exp(x))*diff(diff(diff(diff(y(x),x),x),x),x)+4*(2+exp(x))*diff(diff(diff(y(x),x),x),x)+6*exp(x)*diff(diff(y(x),x),x)+4*exp(x)*diff(y(x),x)+y(x)*exp(x) = 0, y(x))
Maple raw output
[y(x) = x^2/(2*x+exp(x))*_C2+x^3/(2*x+exp(x))*_C1+1/(2*x+exp(x))*_C3*x+1/(2*x+exp(x))*_C4]