Using the Existence & Uniqueness Theorem, determine an interval I on which the following initial value problem has a unique solution. dy/dx = (x-y)1/2 y(2) = 1
Using the Existence & Uniqueness Theorem, determine an interval I on which the following initial value problem has a unique solution. dy/dx = (x-y)1/2 y(2) = 1
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
Using the Existence & Uniqueness Theorem, determine an interval I on which the following initial value problem has a unique solution.
dy/dx = (x-y)1/2
y(2) = 1
Expert Solution
Step 1: Defining the Existence and Uniqueness theorem
We know that for the Initial value problem
Then for the rectangle further assuming is continuous bounded and satisfy Lipschitz condition that is , then the initial value problem has unique solution in the interval where , where
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