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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....
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 Fall '06
 EDeSturler
 Equations, Boundary value problem, Lipschitz continuity, firstorder differential equation

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