Question: Question 12. Consider the differential operator Ly = y(10 + agy + . . . + aly + co, and denote by PL(t) - t10

Question 12. Consider the differential operator Ly = y(10 + agy + . . . + aly + co, and denote by PL(t) - t10 + agt + . . . ait + do its characteristic polynomial. a) Assume pr(t) factors as (r - 1)?(r? +r + 1)*. Find the general solution of the homo- geneous equation Ly = 0. b) Assume PL(t) factors as (72 - 1)5. Find the general solution of the equation Ly = 1. c) Assume pr(t) factors as (r2 + 1) and let y be a solution of the homogeneous equation Ly = 0. Compute lim r By(z). I-+00

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