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examfinalW10 - MATH 216 FINAL EXAM 4 points Please write...

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MATH 216 FINAL EXAM April 23, 2010 Please write your name: 4 points Section: The test contains 8 problems worth 100 points total. To get the full credit you have to show your work . Page 12 contains a table of useful Laplace transforms. 12 Problem Points Score 12 1 2 3 12 4 12 5 12 6 7 12 Total 8 12 12 Typeset by A M S -T E X 1
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Name: ( 12 points ) 1. Problem. Find the solution x ( t ) , y ( t ) to the system of di ff erential equations x = 3 x - 2 y y = 4 x - y satisfying the initial conditions x (0) = 1 and y (0) = - 1. 2
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Name: ( 12 points ) 2. Problem. Find all critical points of the system of di ff erential equations for functions x ( t ) and y ( t ) below and determine their stability x = xy - 3 x y = x + y 2 - 4 . 3
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Name: ( 12 points ) 3. Problem. Match the systems of di ff erential equations for functions x ( t ) and y ( t ) below with their direction fields on the next page. 1) x = y y = x Figure 2) x = x + 2 y y = - 2 x + y Figure 3) x = - y y = x Figure 4) x = 3 x + y y = x + 3 y Figure 5) x = - x + 2 y y = - 2 x - y Figure 6) x = - 3 x + y y = x - 3 y Figure 4
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E –1 –0.5 0 0.5 1 y –1 –0.5 0.5 1 x F –1 –0.5 0 0.5 1 y –1 –0.5 0.5 1 x C –1 –0.5
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