4.45.32 $y^{⁗}(x)+(a^2+b^2)y^{″}(x)+a^2{b}^{2}y(x)=0$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0086521 (sec), leaf count = 34

$$\left\{\{y(x)\to c_4\sin (ax)+c_3\cos (ax)+c_2\sin (bx)+c_1\cos (bx)\}\right\}$$

Maple ✓
cpu = 0.02 (sec), leaf count = 29

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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