Diff Eq Exam and finals

Diff Eq Exam and finals - Do not write here Name: Section...

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Name: Section No. last 4 digits of Soc. Sec. No. Check this box if you do not want your grades emailed to you. 110.302 Diferential Equations Shifman Final Exam 2:00-5:00 p.m., December 13, 2004 One sheet (2 sides, 8 1 2 × 11) of notes may be used during this exam. Tables of integrals and Laplace transforms are also provided. No books, calculators or other materials are permitted. This exam contains 11 pages and has a total of 100 points. Do not write here 1 2 3 4 5 6 7 II Part I. (70 points) Express all answers using real numbers only. (You may use complex numbers in your work, but your answers should not contain i or square roots of negative numbers.) To receive full credit you must show all o± your work and write your answers in the indicated places. 1. (5 points) Find the Laplace transform Y ( s ) of the function y ( t )= 0i f 0 t< 2 t if 2 3 3i f t 3 Answer: Y ( s
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page 2 2. (15 points) a) Find the solution of the linear system: dx 1 dt = 2 x 1 x 2 dx 2 dt =9 x 1 2 x 2 Hint: The roots of the characteristic equation are 2 ± 3 i . Answer:
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page 3 2. (continued) b) Find x 1 ( t ) if the system has initial conditions x 1 (0)=5 ,x 2 (0)=2 .
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Diff Eq Exam and finals - Do not write here Name: Section...

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