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de-practice-final - MAP 2302 PRACTICE FINAL EXAM SPRING...

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MAP 2302 — PRACTICE FINAL EXAM — SPRING 2011 NAMES: GROUP NUMBER Instructions: All work should be written in a proper and coherent manner. Write in such a way that any student in the class can follow your work. When working problems show all your work. Answers with no work or explanations will receive no credit, unless otherwise specified. Each member of a team must submit the solution of a different problem. Do only SIX problems. If you do more than six problems, then the best 6 problems are counted. TOTAL POSSIBLE : 60 points. PART 1 Do no more than 3 questions in Part 1. 1 . [10 pts] Determine those constants m so that ϕ ( x ) = x m is a solution to x 2 y ′′ + 6 xy + 4 y = 0 , assuming x > 0 , and hence find the general solution. Show all reasoning clearly. 2 .[10 pts] Determine whether The Existence and Uniqueness Theorem for First Order Initial Value Problems implies that the Initial Value Problem: dy dx = x 3 + ln y, y (0) = 1 , has a unique solution on some interval containing x = 0. Show all reasoning clearly.
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