4.45.40 $$2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0$$

ODE
$2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0$ ODE Classiﬁcation

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.1551 (sec), leaf count = 52

$\left \{\left \{y(x)\to e^{-x/2} \left ((c_4 x+c_3) \cos \left (\frac {\sqrt {3} x}{2}\right )+(c_2 x+c_1) \sin \left (\frac {\sqrt {3} x}{2}\right )\right )\right \}\right \}$

Maple
cpu = 0.008 (sec), leaf count = 59

$\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\textit {\_C2} \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\textit {\_C3} \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) x +\textit {\_C4} \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) x\right ]$ Mathematica raw input

DSolve[y[x] + 2*y'[x] + 3*y''[x] + 2*y'''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ((C[3] + x*C[4])*Cos[(Sqrt[3]*x)/2] + (C[1] + x*C[2])*Sin[(Sqrt[3]*x)/
2])/E^(x/2)}}

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*exp(-1/2*x)*sin(1/2*3^(1/2)*x)+_C2*exp(-1/2*x)*cos(1/2*3^(1/2)*x)+_C
3*exp(-1/2*x)*sin(1/2*3^(1/2)*x)*x+_C4*exp(-1/2*x)*cos(1/2*3^(1/2)*x)*x]