219 hw3and solution from 2005

Elementary Differential Equations, with ODE Architect CD

  • Homework Help
  • PresidentHackerCaribou10582
  • 2

Info icon This preview shows pages 1–2. Sign up to view the full content.

Math 219, Homework 3 Due date: 9.12.2005, Friday 1. Consider the initial value problem d 2 x dt 2 + dx dt + x = u 4 ( t ) , y (0) = y 0 (0) = 0 (a) Solve this initial value problem using the Laplace transform. (b) Use ODE Architect to solve the equation, and graph the solution. Also graph dx dt with respect to t (You can use the function Step ( t, 4) to create a unit step function with discontinuity at t = 4). (c) Discuss how the graphs agree with the solutions in (a): in particular determine (if any) all the points where x ( t ) and dx dt are discontinuous, behavior of these two functions for t → ∞ , their maxima and minima. 2. Write each of the following systems of differential equations in matrix form, find the eigenvalues and eigenvectors of the coefficient matrices, and using these, find
Image of page 1

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

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: all solutions of each system. Also, graph the phase portraits ( x-y graph) using ODE Architect. Please use a scale which includes the point (0 , 0), and graph several solutions in order to clearly observe the behavior around (0 , 0). Also, place arrows on the solution curves which indicate the direction of increasing t , and make sure that solution curves along the eigenvector directions are graphed if there are any real eigenvectors. (a) dx dt = 2 x-y dy dt = 3 x + 3 y (b) dx dt =-x + y dy dt = 3 x-4 y (c) dx dt = 2 x + 3 y dy dt = 5 x + 5 y (d) dx dt =-4 x + 3 y dy dt =-3 x + 2 y (e) dx dt =-x-3 y dy dt = 2 x + y...
View Full Document

  • '
  • NoProfessor

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern