##### 4.45.44 $$-4 y'''(x)+y''''(x)+12 y''(x)-16 y'(x)+16 y(x)=0$$

ODE
$-4 y'''(x)+y''''(x)+12 y''(x)-16 y'(x)+16 y(x)=0$ ODE Classiﬁcation

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.163764 (sec), leaf count = 42

$\left \{\left \{y(x)\to e^x \left ((c_4 x+c_3) \cos \left (\sqrt {3} x\right )+(c_2 x+c_1) \sin \left (\sqrt {3} x\right )\right )\right \}\right \}$

Maple
cpu = 0.007 (sec), leaf count = 47

$\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right )+\textit {\_C2} \,{\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right )+\textit {\_C3} \,{\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right ) x +\textit {\_C4} \,{\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right ) x\right ]$ Mathematica raw input

DSolve[16*y[x] - 16*y'[x] + 12*y''[x] - 4*y'''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+12*diff(diff(y(x),x),x)-16*diff(y(x),x)+16*y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*exp(x)*sin(3^(1/2)*x)+_C2*exp(x)*cos(3^(1/2)*x)+_C3*exp(x)*sin(3^(1/
2)*x)*x+_C4*exp(x)*cos(3^(1/2)*x)*x]