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(a) Use the energy integral lemma to derive the family of

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 5E Chapter 4.8

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 5E

PROBLEM 5E

(a) Use the energy integral lemma to derive the family of solutions  to the equation

(b) For c  0 show that these solutions are pairwise linearly independent for different values of c in an appropriate interval around t = 0.

(c) Show that none of these solutions satisfies the initial conditions y (0) =1, y’(0)= 2.

Step-by-Step Solution:

Solution

Step 1

In  this problem, we have to derive the family of solution  to the equation .

b) We have to show that pairwise solution is linearly independent.

c)  We have to check the initial conditions whether it satisfies by the solution or not.

Step 2 of 6

Chapter 4.8, Problem 5E is Solved
Step 3 of 6

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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(a) Use the energy integral lemma to derive the family of