Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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
Check Mark
Step 1: Defining the Existence and Uniqueness theorem

We know that for the Initial value problem dydx=fx,y, yx0=y0

Then for  the rectangle R, x-x0≤a, y-y0≤b,further assuming fx,y is continuous bounded and satisfy Lipschitz condition that is dfx,ydy≤k, then the initial value problem has unique solution in the interval x-x0≤h, where h=mina,bM , where fx,y≤M 

 

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