Ordinary Diff Eq Exam Review Solutions 38

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 . ...
View Full Document

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.

Ask a homework question - tutors are online