4.45.25 $y^{⁗}(x)-2y^{″}(x)-8y(x)=0$

ODE
$$y^{⁗}(x)-2y^{″}(x)-8y(x)=0$$ ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00941015 (sec), leaf count = 44

$$\left\{\{y(x)\to c_3{e}^{-2x}+c_4{e}^{2x}+c_2\sin \left(\sqrt{2}x\right)+c_1\cos \left(\sqrt{2}x\right)\}\right\}$$

Maple ✓
cpu = 0.009 (sec), leaf count = 33

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

DSolve[-8*y[x] - 2*y''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)-8*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(2*x)+_C2*exp(-2*x)+_C3*sin(2^(1/2)*x)+_C4*cos(2^(1/2)*x)