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. Consider the n-th order linear differential equation un) + an-1un-1) +...+a1u' + aou = 0, (*) with constant coefficients, whose characteristic polynomial is p(A) = X" + an-1A"-1 +...+ a1^+ ao = 0. Suppose that d; E C occurs with multiplicity k as a root of p. Show that elst, test,…...,t*-1st, are all solutions to (*).

. Consider the n-th order linear differential equation un) + an-1un-1) +...+a1u' + aou = 0, (*) with constant coefficients, whose characteristic polynomial is p(A) = X" + an-1A"-1 +...+ a1^+ ao = 0. Suppose that d; E C occurs with multiplicity k as a root of p. Show that elst, test,…...,t*-1st, are all solutions to (*).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the n-th order linear differential equation: u (n) + an−1u (n−1) + . . . + a1u ′ + a0u = 0, (∗) with constant coefficients, whose characteristic polynomial is p(λ) = λ n + an−1λ n−1 + . . . + a1λ + a0 = 0. Suppose that λj ∈ C occurs with multiplicity k as a root of p. Show that e λj t , teλj t , . . . , tk−1 e λj t , are all solutions to (∗).

. Consider the n-th order linear differential equation u(n) + an-1u(n-1)+...+ aju' + aou = 0, (*) with constant coefficients, whose characteristic polynomial is p(X) = X" + an-1A"-1 + a1d+ ao 0. ... Suppose that d; E C occurs with multiplicity k as a root of p. Show that edst, test,..., ek-1edst, tk-led;t, are all solutions to (*).
Transcribed Image Text:. Consider the n-th order linear differential equation u(n) + an-1u(n-1)+...+ aju' + aou = 0, (*) with constant coefficients, whose characteristic polynomial is p(X) = X" + an-1A"-1 + a1d+ ao 0. ... Suppose that d; E C occurs with multiplicity k as a root of p. Show that edst, test,..., ek-1edst, tk-led;t, are all solutions to (*).
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