a. If p(t) is a polynomial and k a scalar, show that(D - X)(p(t)eu ) = p(r)ex'.b. If
Chapter 9, Problem 38(choose chapter or problem)
a. If p(t) is a polynomial and k a scalar, show that(D - X)(p(t)eu ) = p(r)ex'.b. If p(t) is a polynomial of degree less than m. what is(D - k)m (p(t)ek')?c. Find a basis of the kernel of the linear differential operator {D - k)m. d. If X i.......kr are distinct scalars and m \.........mr are positive integers, find a basis of the kernel of the linear differential operator(O X, )m 1 ...(/) kr)mr.
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