Question: Let L( V) = any() (x) + an- 1y(n -1)(x) + ... + aly'(x) + any(x) where do, a1, ..., an are fixed constants. Consider

Let L( V) = any() (x) + an- 1y(n -1)(x) + ... + aly'(x) + any(x) where do, a1, ..., an are fixed constants. Consider the nth order linear differential equation L(y) = 2es* cos x + 7xe3x (* ) Suppose that it is known that Lly1(x)] = &xe3x when y1(x) = 24xe3x Lly2(x)] = 4es* sin x when y2(x) = 36esx cos x Lly3(x)] = 3es* cosx when y3(x) = 9ex cosx + 18ex sin x Find a particular solution to (*). Enter your answer as a symbolic function of x, as in these Do not include 'y = ' in your answer. examples

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