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31E the equation of Example 5, (a) Does Theorem 1 imply

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

Solution for problem 31E Chapter 1.2

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 31E

?31E the equation of Example 5, (a) Does Theorem 1 imply the existence of a unique solution to (13) that satisfies y(xo) = 0?(b) Show that when equation (13) can’t possibly have a solution in a neighborhood of x = x0 that satisfies y(x0) = 0.(c) Show that there are two distinct solutions to (13) satisfying y(0) = 0 (see Figure 1.4 on page 9).

Step-by-Step Solution:

Solution : Step 1 :In this problem we have to verify the existence of the uniqueness theorem.(a) in this we have to verify the existence of the uniqueness in the given equation.Given the equation is Theorem 1 states that “ consider the initial value problem , If f and are continuous function in some rectangle That contains the point then the initial value problem has a unique solution in some interval where is positive number.”Then find the existence of unique solution to satisfies Consider equation Converted into Then When , then and are not defined.Hence the theorem 1 cannot be applied.

Step 2 of 3

Chapter 1.2, Problem 31E is Solved
Step 3 of 3

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

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31E the equation of Example 5, (a) Does Theorem 1 imply