Chapter 6.2, Problem 30E

To determine

(a)

To derive:

The general solution for the differential equation $y^{(4)}=y$ is

$y=A_1{e}^x+A_2{e}^{-x}+A_3\cos x+A_4\sin x$

To determine

(b)

To derive:

The general solution for the differential equation $y^{(3)}=y$ is

$y=A_1{e}^x+A_2{e}^{\frac{-x}{2}}\cos \left(\frac{\sqrt{3}x}{2}\right)+A_3{e}^{\frac{-x}{2}}\sin \left(\frac{\sqrt{3}x}{2}\right)$