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Math_215_April_2005

Math_215_April_2005 - Be sure this examination has 3 pages...

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Be sure this examination has 3 pages, including one page that just has a table. The University of British Columbia Final Examinations - April 2005 Mathematics 215: Elementary Differential Equations I Section 201 - John Fournier Section 202 - Pichmony Anhaouy Closed book examination. Time: 2.5 hours = 150 minutes. Special Instructions: No aids allowed, except for one coloured letter-size formula sheet. Write your answers in the answer booklet(s). If you use more than one booklet, put your name and the number of booklets used on each booklet. Show enough of your work to justify your answers. 1. (16 points) Compute solutions for the following initial-value problems, and find the largest t -intervals in which those solutions are valid. Could those intervals change if we changed the initial value y (2) to some other number ˆ y (2)? Explain briefly. (a) t dy dt + 3 y = 6 t 3 , y (2) = 8. (b) dy dt + 2 ty 2 = 2 y 2 , y (2) = 8. 2. (16 points) Consider the differential equation 2 y ′′ + 2 y + 0 y = F ( t ) , where one F ( t ) is used in part (a) below, and another is used in the rest of the question.
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