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**Unformatted text preview: **Mathematics 38 Differential Equations Examination 3 April 7, 12:00–1:20 No calculators, notes, or books are allowed. Please make sure all electronic devices you carry are turned off and put away out of sight. Cross out work you do not want graded! Remember to sign your blue book. With your signature you are pledging that you have neither given nor received assistance on this exam. Good luck! 1. (10 points) In parts a. and b. you are given a matrix A , a vector-valued function vector E ( t ) and formulas describing a collection of solutions of the nonhomogeneous system Dvectorx = Avectorx + vector E ( t ) . In each case decide whether the collection is complete. a. A = parenleftbigg- 3- 2 1 parenrightbigg , vector E ( t ) = parenleftbigg 2 e − t- e − t parenrightbigg : braceleftbigg x 1 = 2 c 1 e − 2 t + c 2 e − t x 2 =- c 1 e − 2 t- c 2 e − t + e − t . b. A = 5- 3 3- 5 1 2 , vector E ( t ) = 4 : x 1 = 6 c 1 e 4 t- 2 c 2...

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