# rev3 - MATH 3200 Bennethum Review Problems for Final Exam...

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MATH 3200 Bennethum Review Problems for Final Exam: Laplace Transforms These are practice problems on the Laplace trasform for the final exam. For this exam, two sides of an 8.5x11” sheet of paper will be allowed for notes (it can be on two separate sheets). No technology of any kind will be allowed. The topics covered on this review sheet include material covered in Chapter 5 Kohler and Johnson. Answers are given on the last page. To be included with the exam: Table on forms of particular solution, Laplace transform table. 1. Take the Laplace transform of the following functions: (a) 1 + e t (b) e t h ( t - 2) 2. Take the inverse Laplace transform of the following functions: (a) 5 s 2 + 3 (b) 1 s 2 + 3 s (c) e s s ( s + 1) 3. Solve the following initial value problem two ways: (1) Without using the Laplace transform and (2) Using the Laplace transform. y ′′ + 4 y = sin t, y (0) = 0 , y (0) = 1 4. Consider the following system of linear ordinary differential equations. Find Y 1 ( s ). Do NOT find y 1 ( t ) or y 2 ( t ). y 1 = y 1 + 4 y 2 , y 2 = - y 1 + y 2 + 3 e t y 1 (0) = 3 , y 2 (0) = 0 5. Solve the following equation for y ( t ). The function f ( t ) is not known.

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