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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 xy-plane so there exists a unique solution. Homework:1~15 odd....
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- Fall '06
- Equations, Boundary value problem, Lipschitz continuity, first-order differential equation