# Exam3A - M427K EXAM 3A FALL, 2009 Dr. Schurle Your name:...

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M427K EXAM 3A FALL, 2009 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (10 points) Use the deﬁnition of the Laplace transform of a function to ﬁnd the Laplace transform of the following function. Show all the details of your work. f ( t ) = 0 0 t < 3 2 3 t < 6 0 6 t

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YOUR SCORE: /100 2. Let g ( t ) = ( 1 0 t 2 e - ( t - 2) 2 t . This problem continues onto the next page. (a) (6 points) Sketch an accurate graph of g ( t ) on t 0. (b) (8 points) Use one or more step functions and exponentials to express g ( t ). (c) (6 points) Find the Laplace transform of g ( t ). You may use the table attached at the end of this exam.
L{ y } of the solution y ( t ) of the initial value problem y 00 - 5 y 0 + 6 y = g ( t ); y (0) = 3; y 0 (0) = 5 . 3. (10 points) Solve the following initial value problem, where

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## This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas at Austin.

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Exam3A - M427K EXAM 3A FALL, 2009 Dr. Schurle Your name:...

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