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Unformatted text preview: ODE, Math S3027D Section 001 Summer 2008 Final Exam Name: July 3, 2008 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. You have 3 hours. Problem Possible Points Points Earned 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 TOTAL 100 1 1. Find the inverse Laplace transform of Y ( s ) = 1 s ( s 2 + 4 s + 8) . 2 2. What is the Laplace transform of the solution y ( t ) to 2 y +3 y = sin t + ( t ), y (0) = 1? Dont solve the equation! Im just asking for the Laplace transform of the solution! 3 3. Let A = parenleftbigg a 4 a 3 parenrightbigg for a a real constant and consider the system x = A x . For each of the following conditions, determine all values of a such that the system satisfies the condition. (a) Asymptotically stable (b) Improper node (means there is a repeated eigenvalue but only a 1dimensional space of eigenvectors)....
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 Spring '11
 Peters
 Math, Differential Equations, Equations, Continuous function, Constant of integration, Eigenvalue, eigenvector and eigenspace, upper right quadrant

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