4.46.22 $y^{\prime \prime \prime \prime \prime \prime }(x)+ay(x)=0$

ODE
$$y^{\prime \prime \prime \prime \prime \prime }(x)+ay(x)=0$$ ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0083526 (sec), leaf count = 98

$$\left\{\{y(x)\to c_2{e}^{(-1{)}^{5/6}\sqrt[6]{a}x}+c_3{e}^{-\sqrt[6]{-1}\sqrt[6]{a}x}+c_5{e}^{-(-1{)}^{5/6}\sqrt[6]{a}x}+c_6{e}^{\sqrt[6]{-1}\sqrt[6]{a}x}+c_4\sin \left(\sqrt[6]{a}x\right)+c_1\cos \left(\sqrt[6]{a}x\right)\}\right\}$$

Maple ✓
cpu = 0.013 (sec), leaf count = 102

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{(i\sqrt{3}-1)x}{2}\sqrt[6]{-a}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{(i\sqrt{3}+1)x}{2}\sqrt[6]{-a}}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{(i\sqrt{3}-1)x}{2}\sqrt[6]{-a}}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{\frac{(i\sqrt{3}+1)x}{2}\sqrt[6]{-a}}+\mathit{\_}\mathit{C}\mathit{5}{\mathrm{e}}^{-\sqrt[6]{-a}x}+\mathit{\_}\mathit{C}\mathit{6}{\mathrm{e}}^{\sqrt[6]{-a}x}\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> E^((-1)^(5/6)*a^(1/6)*x)*C[2] + C[3]/E^((-1)^(1/6)*a^(1/6)*x) + C[5]/E
^((-1)^(5/6)*a^(1/6)*x) + E^((-1)^(1/6)*a^(1/6)*x)*C[6] + C[1]*Cos[a^(1/6)*x] + 
C[4]*Sin[a^(1/6)*x]}}

Maple raw input

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

Maple raw output

y(x) = _C1*exp(-1/2*(I*3^(1/2)-1)*(-a)^(1/6)*x)+_C2*exp(-1/2*(I*3^(1/2)+1)*(-a)^
(1/6)*x)+_C3*exp(1/2*(I*3^(1/2)-1)*(-a)^(1/6)*x)+_C4*exp(1/2*(I*3^(1/2)+1)*(-a)^
(1/6)*x)+_C5*exp(-(-a)^(1/6)*x)+_C6*exp((-a)^(1/6)*x)