##### 4.45.18 $$y''''(x)+y''(x)+y(x)=0$$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.154354 (sec), leaf count = 56

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

Maple
cpu = 0.01 (sec), leaf count = 57

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

DSolve[y[x] + y''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(y(x),x),x)+y(x) = 0, y(x))

Maple raw output

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