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# Given any nth-order homogeneous linear differential equation with constant coefficients ISBN: 9780130084514 53

## Solution for problem 14 Chapter 2.7

Linear Algebra | 4th Edition

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Problem 14

Given any nth-order homogeneous linear differential equation with constant coefficients, prove that, for any solution x and any to G R, if x(t0) = x'(to) = = .T(TC_1)(0) = 0, then x = 0 (the zero function). Hint: Use mathematical induction on n as follows. First prove the conclusion for the case n = 1. Next suppose that it is true for equations of order n 1, and consider an nth-order differential equation with auxiliary polynomial p(t). Factor p(t) = q(t)(t c), and let z = q((D))x. Show that z(to) = 0 an d z' cz 0 to conclude that z = 0. Now apply the induction hypothesis.

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FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS I: Introduction and Analytic Methods David Levermore Department of Mathematics University of Maryland 22 January 2012 Because the presentation of this material in lecture will diﬀer from that in the book, I felt that notes that closely follow the lecture presentation might be appreciated. Contents 1. Introduction: Classiﬁcation and Overview 1.1. Classiﬁcation 2 1.2. Course Overview 4 2. First-Order Equat

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##### ISBN: 9780130084514

The answer to “Given any nth-order homogeneous linear differential equation with constant coefficients, prove that, for any solution x and any to G R, if x(t0) = x'(to) = = .T(TC_1)(0) = 0, then x = 0 (the zero function). Hint: Use mathematical induction on n as follows. First prove the conclusion for the case n = 1. Next suppose that it is true for equations of order n 1, and consider an nth-order differential equation with auxiliary polynomial p(t). Factor p(t) = q(t)(t c), and let z = q((D))x. Show that z(to) = 0 an d z' cz 0 to conclude that z = 0. Now apply the induction hypothesis.” is broken down into a number of easy to follow steps, and 108 words. Since the solution to 14 from 2.7 chapter was answered, more than 253 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 43 chapters, and 881 solutions. Linear Algebra was written by and is associated to the ISBN: 9780130084514. This textbook survival guide was created for the textbook: Linear Algebra , edition: 4. The full step-by-step solution to problem: 14 from chapter: 2.7 was answered by , our top Math solution expert on 07/25/17, 09:33AM.

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Given any nth-order homogeneous linear differential equation with constant coefficients