4.45.29 $y^{⁗}(x)+a^2{y}^{″}(x)=0$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0268292 (sec), leaf count = 34

$$\left\{\{y(x)\to -\frac{c_2\sin (ax)}{a^2}-\frac{c_1\cos (ax)}{a^2}+c_{4}x+c_3\}\right\}$$

Maple ✓
cpu = 0.013 (sec), leaf count = 21

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

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

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+a^2*diff(diff(y(x),x),x) = 0, y(x),'implicit')

Maple raw output

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