4.45.30 $y^{⁗}(x)+a^{4}y(x)+2a^2{y}^{″}(x)=0$

ODE
$$y^{⁗}(x)+a^{4}y(x)+2a^2{y}^{″}(x)=0$$ ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00831964 (sec), leaf count = 30

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

Maple ✓
cpu = 0.011 (sec), leaf count = 25

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

DSolve[a^4*y[x] + 2*a^2*y''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

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) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C4*x+_C2)*cos(a*x)+sin(a*x)*(_C3*x+_C1)