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5. Consider the initial value problem ²y" – ty' + y = 0, y(1) = 1, y'(1) = 1. (a) What is the largest interval on which Theorem 3.1 guarantees the existence of a unique solution? (b) Show by direct substitution that the function y(t) =tis the unique solution of this initial value problem. What is the interval on which this solution actually exists? (c) Does this example contradict the assertion of Theorem 3.1? Explain.

5. Consider the initial value problem ²y" – ty' + y = 0, y(1) = 1, y'(1) = 1. (a) What is the largest interval on which Theorem 3.1 guarantees the existence of a unique solution? (b) Show by direct substitution that the function y(t) =tis the unique solution of this initial value problem. What is the interval on which this solution actually exists? (c) Does this example contradict the assertion of Theorem 3.1? Explain.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer please #5 parts a b and c

 

 

(section 3.1)

5. Consider the initial value problem t’y" – ty' + y = 0, y(1) = 1, y'(1) = 1. (a) What is the largest interval on which Theorem 3.1 guarantees the existence of a unique solution? (b) Show by direct substitution that the function y(t) = t is the unique solution of this initial value problem. What is the interval on which this solution actually exists? (c) Does this example contradict the assertion of Theorem 3.1? Explain.
Transcribed Image Text:5. Consider the initial value problem t’y" – ty' + y = 0, y(1) = 1, y'(1) = 1. (a) What is the largest interval on which Theorem 3.1 guarantees the existence of a unique solution? (b) Show by direct substitution that the function y(t) = t is the unique solution of this initial value problem. What is the interval on which this solution actually exists? (c) Does this example contradict the assertion of Theorem 3.1? Explain.
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