Show that there is a change of variables that converts the nth order differential

Chapter 4, Problem 4.6.70

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Show that there is a change of variables that converts the nth order differential equation into a system of n linear differential equations whose coefficient matrix is the companion matrix C( p) of the polynomial p(l) ln an1ln1 p a1l a0. [The notation x(k) denotes the kth derivative of x. See Exercises 2632 in Section 4.3 for the definition of a companion matrix.]

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