math20D spring 2009 final

math20D spring 2009 final - Name: PID: TA: Sec. No: Sec....

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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20D. Final Examination December 9, 2008 Turn off and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 10 2 10 3 10 4 8 5 8 6 10 56 1. Consider the following differential equation: y 00- xy- y = 0 . (a) (6 points) Find the recurrence relation for the power series solution about the point x = 0. (b) (4 points) Write the first four terms of each of the two linearly independent power series solutions. 2. (10 points) Use the Laplace transform to solve the following initial value problem: y 00 + 9 y = ( t- 3) y (0) = 0 , y (0) = 3 Refer to the attached table of Laplace transforms. 3. Consider the following homogeneous linear system of differential equations:3....
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math20D spring 2009 final - Name: PID: TA: Sec. No: Sec....

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