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finalexamsolutions - Math 527, Final Exam, (Sample...

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Unformatted text preview: Math 527, Final Exam, (Sample Solutions) University of New Hampshire Fall 2007 NAME: Section: Please complete any 5 of the 7 problems provided. Cross out the problem you do not want graded in the table below. In cases of ambiguity, we will grade the first four problems . This exam is closed calculator, and closed neighbor. You are permitted one full page of self-produced notes/examples. Your crib sheet must be passed in with your exam. Any electronically reproduced crib sheets (xerox copies, printer copies of the same or suspiciously similar documents) will result in an immediate failure on this exam (i.e. 0 points). Crib sheets will be returned with the graded exams except in cases of questionable authorship, where the crib sheets will be retained as evidence. A small table of Laplace transforms is provided on the last page. No collaboration is permitted. If you have any questions, please raise your hand. Question Points Possible 1 20 2 20 3 20 4 20 5 20 6 20 7 20 1 1. Consider the following initial value problem: y- 2 y = t 2 e 2 t , y (0) = 1 (a) Use the method of integrating factors to solve this problem and find the exact solution. d dt [ e- 2 t y ] = t 2 y = t 3 3 e 2 t + Ce 2 t Applying the initial condition yields C = 1 (b) Describe the behavior of this solution in the limit that t . This solution grows without bound as t 2 2. Two isotopes of the same radioactive element are observed to decay at rates pro-2....
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finalexamsolutions - Math 527, Final Exam, (Sample...

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