4.45.21 $y^{⁗}(x)+2y^{″}(x)+y(x)=\cos (x)$

ODE
$$y^{⁗}(x)+2y^{″}(x)+y(x)=\cos (x)$$ ODE Classification

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0580983 (sec), leaf count = 43

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

Maple ✓
cpu = 0.164 (sec), leaf count = 33

$$\{y\left(x\right)=\frac{(8\mathit{\_}\mathit{C}\mathit{3}x-x^2+8\mathit{\_}\mathit{C}\mathit{1}+2)\cos \left(x\right)}{8}+\sin \left(x\right)((\mathit{\_}\mathit{C}\mathit{4}+\frac{3}{8})x+\mathit{\_}\mathit{C}\mathit{2})\}$$ 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),'implicit')

Maple raw output

y(x) = 1/8*(8*_C3*x-x^2+8*_C1+2)*cos(x)+sin(x)*((_C4+3/8)*x+_C2)