Method of Annihilators. In 20 through 22, we consider
Chapter 4, Problem 22(choose chapter or problem)
Method of Annihilators. In 20 through 22, we consider another way of arriving atthe proper form of Y(t) for use in the method of undetermined coefficients. The procedureis based on the observation that exponential, polynomial, or sinusoidal terms (or sums andproducts of such terms) can be viewed as solutions of certain linear homogeneous differentialequations with constant coefficients. It is convenient to use the symbol D for d/dt. Then, forexample, et is a solution of (D + 1)y = 0; the differential operator D + 1 is said to annihilate,or to be an annihilator of, et. In the same way, D2 + 4 is an annihilator of sin 2t or cos 2t,(D 3)2 = D2 6D + 9 is an annihilator of e3t or te3t, and so forth.Use the method of annihilators to find the form of a particular solution Y(t)
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