find the longest interval in which the following initial value problem is guaranteed to have a unique solution. (t + 1)g′′−√(16 −t^2)g′+ g = −t^3, g(−2) = 2, g′(−2) = −3.
find the longest interval in which the following initial value problem is guaranteed to have a unique solution. (t + 1)g′′−√(16 −t^2)g′+ g = −t^3, g(−2) = 2, g′(−2) = −3.
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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Question
find the longest interval in which
the following initial value problem is guaranteed to have a unique solution.
(t + 1)g′′−√(16 −t^2)g′+ g = −t^3, g(−2) = 2, g′(−2) = −3.
Expert Solution
Step 1 Existence and Uniqueness theorem for second order linear IVP
Consider the initial value problem
If are continuous functions on an interval I containing , then there is exactly one solution of this IVP throughout the interval I
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