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practice-test1

# practice-test1 - MAP 2302 PRACTICE MID-TERM EXAM SPRING...

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MAP 2302 — PRACTICE MID-TERM EXAM — SPRING 2011 NAME 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. (1) [ 10 points ] Determine whether the Existence Uniqueness Theorem implies that the Initial Value Problem dy dx = 1 x - y - 1 , y (2) = 1 , has a unique solution on some interval containing x = 2. (2) [8 + 2 = 10 points ] (i) Solve the Initial Value Problem dy dx = x + 2 y, y (0) = 0 . (ii) Below is the direction field plot for the differential equation dy dx = x + 2 y. –2 –1 0 1 2 y(x) –2 –1 1 2 x Plot the solution to the initial value problem (in (i)) on this direction field plot. (3) [ 10 points ] Solve the following initial value problem. Your solution y should be given explicitly in terms of x . dy dx + y 3 e sin x cos x = 0 , y (0) = 1 . 1

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practice-test1 - MAP 2302 PRACTICE MID-TERM EXAM SPRING...

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