Ordinary Diff Eq Exam Review Solutions 78

Ordinary Diff Eq Exam Review Solutions 78 - 80 1 Solutions...

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Unformatted text preview: 80 1 Solutions 35. 36. 37. 38. 39. with 40. and . Thus, and with 41. with . But since, for any natural number , lower degree terms. Thus translating the highest power of found in will produce the same highest power of in . Since the same is also true for , it follows that . Thus, is a proper rational function. 42. If then where . Then and . Hence is a proper rational function. 43. Suppose but not in where does not have a factor of rule we have Thus . Then we can write . By the quotient . Suppose . Then the numerator has a factor of . But this implies has a factor of . But this is impossible since . Hence . ...
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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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