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Homework Help: Answer check: differential initial value problem

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data
    solve the IVP



    2. Relevant equations

    3. The attempt at a solution

    auxiliary equation:
    so we have r=4 with m=2

    y(x)= c1e4x+c2xe4x

    y(0)--> c1e0 + 0 = 2
    now we have:

    take first derivative
    y'(x) = 8e4x+c2e4x+4c2xe4x (product rule)

    y'(0) ----> 8e0+c2e0+ 0 = 7

    so our final equation is:


    Everything seems ok, but just wanted to run it by here to make sure it's all done correctly. thanks all!
  2. jcsd
  3. Apr 26, 2009 #2
    Looks fine to me
  4. Apr 27, 2009 #3


    Staff: Mentor

    It's much easier to check that a potential solution actually works than it is to get the solution. For your problem all you need to do are the following:
    1. Verify that y(x) = 2e4x + xe4x satisfies y'' - 8y' + 16y = 0.
    2. Verify that y(0) = 2.
    3. Verify that y'(0) = 7.

    If your solution satisfies the differential equation and initial conditions, you can bask in the warm glow of confidence that you nailed that problem.
  5. Apr 27, 2009 #4
    ......I didn't even think of trying that. Thanks guys!
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