This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: a x b , c y d containing the point , x y in the interior. If , f x y and / f y are continuous on R , then there exist an interval I centered at x and a unique function y x defined on I satisfying the IVP. If the condition does not hold, the IVP may have no solution or more than one solution. Ex3. Using Theorem 2.1 The theorem guarantees that there exists an interval about x on which 2 x y e is the only solution of the initial value problem of , 2 y y y . It is clear that , , / 1 f x y y f y are continuous everywhere on the xyplane so there exists a unique solution. Homework:1~15 odd....
View
Full
Document
This note was uploaded on 04/01/2008 for the course MATH 2214 taught by Professor Edesturler during the Fall '06 term at Virginia Tech.
 Fall '06
 EDeSturler
 Equations

Click to edit the document details