4.45.15 $y^{⁗}(x)=y(x)+e^x\cos (x)$

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

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.066143 (sec), leaf count = 38

$$\left\{\{y(x)\to c_1{e}^x+c_3{e}^{-x}+c_4\sin (x)+(c_2-\frac{e^x}{5})\cos (x)\}\right\}$$

Maple ✓
cpu = 0.096 (sec), leaf count = 31

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-x}+\frac{(5\mathit{\_}\mathit{C}\mathit{1}-{\mathrm{e}}^x)\cos \left(x\right)}{5}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{3}\sin \left(x\right)\}$$ Mathematica raw input

DSolve[y''''[x] == E^x*Cos[x] + y[x],y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = _C4*exp(-x)+1/5*(5*_C1-exp(x))*cos(x)+_C2*exp(x)+_C3*sin(x)