(a) Assume that Theorem 7 3 1 holds when the symbol a is replaced by ki, where k is a real number and i 2 1 Show that te kti can be used to deduce (b) Now use the Laplace transform to solve the initial value problem x ' ' 2 x cos t, x(0) 0, '(0) 0 Theorem 7 3 1 If f(t) F(s) and a is any real number...

a From theorem 76 Lite because L1e1e ds d 1 ds ski 1 ski 1 ski Now by Eu ...

(a) Assume that Theorem 7.3.1 holds when the symbol a is replaced by ki, where k is...

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(a) Assume that Theorem 7.3.1 holds when the symbol a is replaced by ki, where k is a real number and i² = -1. Show that ℒ{te^kti} can be used to deduce

- k L{t cos kt} (s? + k2)? 2ks L{t sin kt} (s? + k)2

(b) Now use the Laplace transform to solve the initial value problem x'' + ω²x = cos ωt, x(0) = 0, '(0) = 0.

Theorem 7.3.1

If ℒ{f(t)} = F(s) and a is any real number, then

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A First Course in Differential Equations with Modeling Applications

ISBN: 978-1111827052

10th edition

Authors: Dennis G. Zill

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Question Posted: Nov 02, 2020 04:33 AM

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(a) Assume that Theorem 7.3.1 holds when the symbol a is replaced by ki, where k is...

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- k L{t cos kt} (s? + k2)? 2ks L{t sin kt} (s? + k)2"

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a From theorem 76 Lite because L1e1e ds d 1 ds ski 1 ski 1 ski Now by Eu...View the full answer

A First Course in Differential Equations with Modeling Applications

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