Ordinary Diff Eq Exam Review Solutions 38

Ordinary Diff Eq Exam Review Solutions 38 - 40 1 Solutions...

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Unformatted text preview: 40 1 Solutions Comparing to order 3. to the exact solution, we see that the series agree up 17. Let . Then . Let and be arbitrary real numbers. Then by the mean value theorem there is a number in between and such that It follows that is Lipschitz on any strip. Theorem 10 implies there is a unique solution on all of . 18. Let . Since and are continuous on it follows that is continuous on the strip . Further more is bounded: i.e. there is a number such that , for all . Let and and be arbitrary real numbers. Then It follows that 10, interval . is Lipschitz with Lipschitz constant . By Theorem has a unique solution on the entire 19. 1. First assume that standard form becomes . Then is linear and in . An integrating factor is and multiplying both sides by gives . This simpliﬁes to . Now integrate to get or . We observe that this solution is also valid for . Graphs are given below for various values of . ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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