Consider the two-parameter family of functions defined by y=C1e2x+C2e−2x, where C1 and C2 are arbitrary real constants.
a. Part 1: Compute the first and second derivatives of the general member of the family.
b. Part 2: Show that every member of the family satisfies the relation y′′−4y=0.
c. Part 3: Give a clear argument that the differential equation obtained in part (b) is of the lowest possible order for which all members of the given family are solutions.