##### 4.45.27 $$y''''(x)+5 y''(x)+6 y(x)=0$$

ODE
$y''''(x)+5 y''(x)+6 y(x)=0$ ODE Classiﬁcation

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.147644 (sec), leaf count = 50

$\left \{\left \{y(x)\to c_3 \cos \left (\sqrt {2} x\right )+c_1 \cos \left (\sqrt {3} x\right )+c_4 \sin \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {3} x\right )\right \}\right \}$

Maple
cpu = 0.008 (sec), leaf count = 37

$\left [y \left (x \right ) = \textit {\_C1} \sin \left (\sqrt {2}\, x \right )+\textit {\_C2} \cos \left (\sqrt {2}\, x \right )+\textit {\_C3} \sin \left (\sqrt {3}\, x \right )+\textit {\_C4} \cos \left (\sqrt {3}\, x \right )\right ]$ Mathematica raw input

DSolve[6*y[x] + 5*y''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(y(x),x),x)+6*y(x) = 0, y(x))

Maple raw output

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