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2. Consider the initial value problem (IVP) { (t +1)(t – 1)(t- 2) t e"y y(.5) - cos t? %3D 1 Use Theorem 2.5.1 to determine the interval in which this IVP has unique solution. (Do not try to solve).

2. Consider the initial value problem (IVP) { (t +1)(t – 1)(t- 2) t e"y y(.5) - cos t? %3D 1 Use Theorem 2.5.1 to determine the interval in which this IVP has unique solution. (Do not try to solve).

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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Theorem 2.5.1: Consider the 1st-order Linear IVP Sy' + p(t)y = g(t) (3) y(to) = yo Assume p(t), g(t) are continuous on an interval /: a <t < B and to is in 1. Then, • The IVP (3) has a solution y = p(t). • The domain of y = y(t) is I. • The solution y = p(t) is unique, on /. %3D %3D
Transcribed Image Text:Theorem 2.5.1: Consider the 1st-order Linear IVP Sy' + p(t)y = g(t) (3) y(to) = yo Assume p(t), g(t) are continuous on an interval /: a <t < B and to is in 1. Then, • The IVP (3) has a solution y = p(t). • The domain of y = y(t) is I. • The solution y = p(t) is unique, on /. %3D %3D
2. Consider the initial value problem (IVP) 了(t+ 1)(t-1)(t-2)+eg y(.5) cos t? 1 Use Theorem 2.5.1 to determine the interval in which this IVP has unique solution. (Do not try to solve).
Transcribed Image Text:2. Consider the initial value problem (IVP) 了(t+ 1)(t-1)(t-2)+eg y(.5) cos t? 1 Use Theorem 2.5.1 to determine the interval in which this IVP has unique solution. (Do not try to solve).
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