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Homework Help: A system of 1st order diffy q's

  1. Mar 31, 2010 #1
    1. The problem statement, all variables and given/known data

    Transform the given initial value problem into an initial value problem for the first two first order equations.

    u'' + .25u' + 4u = 2cos(3t), u(0)=1, u'(0)=-2

    2. Relevant equations

    Nothing, really.

    3. The attempt at a solution

    x1=u , x2=u' => x2' = -.25x2 -4x1 + 2cos(3t); x1'=x2

    There's the system. I don't understand the initial value part, though; and my professor didn't do any examples.

    I know x1 and x2 are functions of t, so the second equation is saying that the derivative of x1 is x2, and x1'(0)=x2(0)=-2; x1(0)=1. Where do I go from here?
     
  2. jcsd
  3. Mar 31, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You don't go anywhere from there. The problem asked to change the u(t) equation into a coupled initial value problem for two first order equations. I think you did that with your x1(t) and x2(t).
     
  4. Mar 31, 2010 #3
    I didn't read the problem! Hahaha!
     
  5. Apr 1, 2010 #4

    Mark44

    Staff: Mentor

    If all else fails, read the instructions:smile:
     
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