M251ex2(sp09)

# M251ex2(sp09) - MATH 251 Examination II April 7 2009 Name...

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Unformatted text preview: MATH 251 Examination II April 7, 2009 Name: Student Number: Section: This exam has 16 questions for a total of 100 points. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work. The point value for each question is in parentheses to the right of the question number. A table of Laplace transforms is attached as the last page of the exam. PLEASE TURN OFF AND PUT AWAY YOUR CELL PHONE. YOU MAY NOT USE A CALCULATOR ON THIS EXAM. 1 thru 3 : 4 thru 13: 14: 15: 16: Total: Do not write in this box. MATH 251 EXAMINATION II April 7, 2009 1. (5 points) Match the sketches of phase portraits for the 2x2 linear systems x ′ = Ax , lettered A through F, with the names of their critical points at the origin. (A) (B) y-2-1.5-1-0.5 0.5 1 1.5 2 x-2-1.5-1-0.5 0.5 1 1.5 2 y-2-1.5-1-0.5 0.5 1 1.5 2 x-2-1.5-1-0.5 0.5 1 1.5 2 (C) (D) y-2-1.5-1-0.5 0.5 1 1.5 2 x-2-1.5-1-0.5 0.5 1 1.5 2 y-2-1.5-1-0.5 0.5 1 1.5 2 x-2-1.5-1-0.5 0.5 1 1.5 2 (E) (F) y-2-1.5-1-0.5 0.5 1 1.5 2 x-2-1.5-1-0.5 0.5 1 1.5 2 y-2-1.5-1-0.5 0.5 1 1.5 2 x-2-1.5-1-0.5 0.5 1 1.5 2 node: center: proper node (star point): saddle point: spiral point: Page 2 of 11 MATH 251 EXAMINATION II April 7, 2009 2. (5 points) Match the following general solutions of 2x2 linear systems x ′ = Ax with the sketches of the phase portraits given in Problem 1: (a) e − t parenleftbigg C 1 bracketleftbigg 1 2 bracketrightbigg + C 2 bracketleftbigg t + 1 2 t + 1 bracketrightbiggparenrightbigg (b) C 1 e − t bracketleftbigg 1 2 bracketrightbigg + C 2 e − 2 t bracketleftbigg 2 1 bracketrightbigg (c) C 1 e − t bracketleftbigg 1 bracketrightbigg + C 2 e − t bracketleftbigg 1 bracketrightbigg...
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M251ex2(sp09) - MATH 251 Examination II April 7 2009 Name...

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