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(21) (a) verify that y1(t) : =t and y2(t) :=t3are two

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

Solution for problem 27E Chapter 4.7

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 27E

Consider the linear equation (21) (a) verify that y1(t) : =t and y2(t) :=t3are two solutions to (21) on Furthermore, show that for t0=1.(b) Prove that y1(t) and y2(t) are linearly independent on (c) Verify that the function y3(t) : = |t|3 is also a solution to (21) on (d) Prove that there is no choice of constants c1, c2 such that assumption leads to a contradiction.](e) From parts (c) and (d), we see that there is at least one solution to (21) on that is not expressible as a linear combination of the solutions y1(t),y2(t) . Does this provide a counterexample to the theory in this section? Explain

Step-by-Step Solution:

Solution:Step 1: In this problem, we have to consider the linear equation

Step 2 of 2

Chapter 4.7, Problem 27E is Solved
Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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(21) (a) verify that y1(t) : =t and y2(t) :=t3are two

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