##### 4.45.16 $$y''''(x)+a y(x)=0$$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.148057 (sec), leaf count = 76

$\left \{\left \{y(x)\to c_1 e^{(-1)^{3/4} \sqrt [4]{a} x}+c_2 e^{-\sqrt [4]{-1} \sqrt [4]{a} x}+c_3 e^{-(-1)^{3/4} \sqrt [4]{a} x}+c_4 e^{\sqrt [4]{-1} \sqrt [4]{a} x}\right \}\right \}$

Maple
cpu = 0.024 (sec), leaf count = 50

$\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-i \left (-a \right )^{\frac {1}{4}} x}+\textit {\_C2} \,{\mathrm e}^{i \left (-a \right )^{\frac {1}{4}} x}+\textit {\_C3} \,{\mathrm e}^{-\left (-a \right )^{\frac {1}{4}} x}+\textit {\_C4} \,{\mathrm e}^{\left (-a \right )^{\frac {1}{4}} x}\right ]$ Mathematica raw input

DSolve[a*y[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = _C1*exp(-I*(-a)^(1/4)*x)+_C2*exp(I*(-a)^(1/4)*x)+_C3*exp(-(-a)^(1/4)*x)+
_C4*exp((-a)^(1/4)*x)]