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Homework Help: First-Order Differential Equation

  1. Jan 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Find x(t) given the following:
    From here I get stuck. I know I can integrate it, but then I have another constant?
  2. jcsd
  3. Jan 10, 2012 #2


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    No, no. Your last line should read,


    You can't just move the e^(-4t) inside the integral like that. Now sure, integrate it. If you add another constant, does it matter?
  4. Jan 10, 2012 #3

    Then, since
    we have
    Now if I combine these constant to make a new one, that doesn't really help me out in regards to the equation does it?
  5. Jan 10, 2012 #4


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    Why not integrate the right hand side ?
  6. Jan 10, 2012 #5
    @ Sammy:
    I was doing that before, but I could not seem to get the answer. I just tried again given the information Dick presented and got the right answer. Thanks!
  7. Jan 10, 2012 #6


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    is the same as


    You may as well just call C=C1+C2. The extra constant doesn't do anything different than the first one did.
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