4.45.14 $y^{⁗}(x)=y(x)+\cos (x)$

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

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0412753 (sec), leaf count = 40

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

Maple ✓
cpu = 0.063 (sec), leaf count = 35

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

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

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x) = y(x)+cos(x), y(x),'implicit')

Maple raw output

y(x) = _C4*exp(-x)+1/4*(4*_C1-1)*cos(x)+1/4*(-x+4*_C3)*sin(x)+_C2*exp(x)