Find all real-valued solutions to the following differential equation: 16x (5)
(t)+8π 2
x ′′′
(t)+π 4
x ′
(t)=0. (a) Now, find all (real-valued) solutions that satisfy the initial conditions at t=1 : x(1)=1,x ′
(1)= 2
π
​
. (b) Find all (real-valued) solutions satisfying the following initial conditions: x (k)
(1)=( 2
π
​
) k
(cos( 2
πk
​
)+sin( 2
πk
​
)),k∈{0,1,…,4}.