Consider the following ODE: p(D)x = ƒ, where p(r) is the degree 2 polynomial p(r) d Let f(t) = est. We will assume that b, c, s are all real numbers. dt p2 + br + c and D (a) Give non-zero values for...

Extracted text: Consider the following ODE: p(D)x = ƒ, where p(r) is the degree 2 polynomial p(r) d Let f(t) = est. We will assume that b, c, s are all real numbers. dt p2 + br + c and D (a) Give non-zero values for b, c and s such that xp(t) : particular solution of the ODE p(D)x = f. (b) Give non-zero values for 6, c, s, where g(t) = est and x(t) is the unique solution of the ODE p(D)x = g with initial conditions f(t) for all t E R, where xp(t) is a and also give values for u, v, such that x(t) = g(t) for all t e R, x(0) = u and x' (0) = v.