##### 4.45.21 $$y''''(x)+2 y''(x)+y(x)=\cos (x)$$

ODE
$y''''(x)+2 y''(x)+y(x)=\cos (x)$ ODE Classiﬁcation

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica
cpu = 0.18343 (sec), leaf count = 43

$\left \{\left \{y(x)\to \left (-\frac {x^2}{8}+c_2 x+\frac {5}{16}+c_1\right ) \cos (x)+\frac {1}{4} (x+4 c_4 x+4 c_3) \sin (x)\right \}\right \}$

Maple
cpu = 1.143 (sec), leaf count = 38

$\left [y \left (x \right ) = \left (-\frac {x^{2}}{8}+\frac {1}{4}\right ) \cos \left (x \right )+\frac {3 x \sin \left (x \right )}{8}+\textit {\_C1} \cos \left (x \right )+\textit {\_C2} \sin \left (x \right )+\textit {\_C3} x \cos \left (x \right )+\textit {\_C4} x \sin \left (x \right )\right ]$ Mathematica raw input

DSolve[y[x] + 2*y''[x] + y''''[x] == Cos[x],y[x],x]

Mathematica raw output

{{y[x] -> (5/16 - x^2/8 + C[1] + x*C[2])*Cos[x] + ((x + 4*C[3] + 4*x*C[4])*Sin[x
])/4}}

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+y(x) = cos(x), y(x))

Maple raw output

[y(x) = (-1/8*x^2+1/4)*cos(x)+3/8*x*sin(x)+_C1*cos(x)+_C2*sin(x)+_C3*x*cos(x)+_C
4*x*sin(x)]