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
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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 dydx=fx,y, yx0=y0

Then for  the rectangle R, x-x0a, y-y0b,further assuming fx,y is continuous bounded and satisfy Lipschitz condition that is dfx,ydyk, then the initial value problem has unique solution in the interval x-x0h, where h=mina,bM , where fx,yM 

 

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