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**Unformatted text preview: **Mathematics 38 Differential Equations Final Examination May 5, 8:3010:30 No calculators, notes, or books are allowed. Please make sure all electronic devices are turned off and out of sight. Show all work and 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. (15 points) a. Find the general solution of Dvectorx = parenleftbigg 2- 1 3 parenrightbigg vectorx + parenleftbigg e t e t parenrightbigg . You may use that the general solution of the associated homogeneous system is c 1 parenleftbigg 2 e t e t parenrightbigg + c 2 parenleftbigg e 2 t e 2 t parenrightbigg . b. Find the general solution of x + x = sin 3 t . c . Find the general solution of tx = ( x + 1)( t 2 + 1) for t > . 2. (5 points) Calculate the inverse Laplace transform of s 3( s 2 + 9) 2 ....

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