4.45.31 $y^{⁗}(x)+a^{4}y(x)+2a^2{y}^{″}(x)=\cosh (ax)$

ODE
$$y^{⁗}(x)+a^{4}y(x)+2a^2{y}^{″}(x)=\cosh (ax)$$ ODE Classification

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.251201 (sec), leaf count = 47

$$\left\{\{y(x)\to \frac{4a^4((c_{4}x+c_3)\sin (ax)+(c_{2}x+c_1)\cos (ax))+\cosh (ax)}{4a^4}\}\right\}$$

Maple ✓
cpu = 0.496 (sec), leaf count = 51

$$\{y\left(x\right)=\frac{{\mathrm{e}}^{-ax}+(8\mathit{\_}\mathit{C}\mathit{3}x+8\mathit{\_}\mathit{C}\mathit{1})a^4\cos \left(ax\right)+(8\mathit{\_}\mathit{C}\mathit{4}x+8\mathit{\_}\mathit{C}\mathit{2})a^4\sin \left(ax\right)+{\mathrm{e}}^{ax}}{8a^4}\}$$ Mathematica raw input

DSolve[a^4*y[x] + 2*a^2*y''[x] + y''''[x] == Cosh[a*x],y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*a^2*diff(diff(y(x),x),x)+a^4*y(x) = cosh(a*x), y(x),'implicit')

Maple raw output

y(x) = 1/8*(exp(-a*x)+(8*_C3*x+8*_C1)*a^4*cos(a*x)+(8*_C4*x+8*_C2)*a^4*sin(a*x)+
exp(a*x))/a^4