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 = 0.0519453 (sec), leaf count = 0 , could not solve
DSolve[E^x*y[x] + 4*E^x*Derivative[1][y][x] + 6*E^x*Derivative[2][y][x] + 4*(2 + E^x)*Derivative[3][y][x] + (E^x + 2*x)*Derivative[4][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.017 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{3}+{\it \_C2}\,{x}^{2}+{\it \_C3}\,x+{\it \_C4}}{2\,x+{{\rm e}^{x}}}} \right \} \] 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
DSolve[E^x*y[x] + 4*E^x*Derivative[1][y][x] + 6*E^x*Derivative[2][y][x] + 4*(2 + E^x)*Derivative[3][y][x] + (E^x + 2*x)*Derivative[4][y][x] == 0, y[x], 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),'implicit')
Maple raw output
y(x) = (_C1*x^3+_C2*x^2+_C3*x+_C4)/(2*x+exp(x))