4.45.22 $y^{⁗}(x)-2y^{″}(x)+y(x)=\cos (x)$

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

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0979871 (sec), leaf count = 42

$$\left\{\{y(x)\to e^{-x}(c_{2}x+c_3{e}^{2x}+c_4{e}^{2x}x+c_1)+\frac{\cos (x)}{4}\}\right\}$$

Maple ✓
cpu = 0.028 (sec), leaf count = 31

$$\{y\left(x\right)=\frac{\cos \left(x\right)}{4}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-x}+\mathit{\_}\mathit{C}\mathit{3}x{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{4}x{\mathrm{e}}^{-x}\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (C[1] + x*C[2] + E^(2*x)*C[3] + E^(2*x)*x*C[4])/E^x + Cos[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) = 1/4*cos(x)+_C1*exp(x)+_C2*exp(-x)+_C3*x*exp(x)+_C4*x*exp(-x)