final_spring04

final_spring04 - Student Name: Answers MA-366, Spring 2004,...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
MA-366, Spring 2004, Final Exam Student Name: Answers Note: You may use scratch paper. All solutions and answers must be on those sheets in the space provided. If the space provided is not enough, continue on the back or attach additional sheets (well organized). You must show your work. Two sheets of handwritten notes are allowed. No calculators. Problem # Max Score 1 12 2 12 3 12 4 18 5 12 6 27 7 12 8 12 9 12 10 12 TOTAL 141 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA-366, Spring 2004, Final Exam 2 Problem 1. (12 pts) Solve the system x 0 D ± ± 3 ± 1 ± 1 ± 3 ² x , x (0) D ± 4 1 ² . Plot the solution in the x 1 x 2 -plane. Show the directions along the trajectoriy. What is the type of the zero solution? Is it stable? Answer: x D 3 2 e ± 2t ± 1 ± 1 ² C 5 2 e ± 4t ± 1 1 ² , the zero is a stable node.
Background image of page 2
MA-366, Spring 2004, Final Exam 3 Problem 2. (12 pts) Find the general solution of the system: x 0 D 0 @ 30 0 5 ± 20 00 3 1 A x What can you say about the stability of the zero solution? Answer: x D c 1 e ± 2t 0 @ 0 1 0 1 A C c 2 e 3t 0 @ 1 1 0 1 A C c 3 e 3t 0 @ 0 0 1 1 A . The zero solution is unstable because some of the eigenvalues are positive.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA-366, Spring 2004, Final Exam 4 Problem 3. (12 pts) Find the general solution of the system: x 0 D ± 11 ± 41 ² x Sketch the phase portrait of the system. Show clearly the directions. What is the type of the zero solution? Is it stable?
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 13

final_spring04 - Student Name: Answers MA-366, Spring 2004,...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online