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Differential Equations Intro material

  1. Aug 30, 2012 #1
    1. The problem statement, all variables and given/known data

    What function do you know from calculus is such that its first derivative is a constant multiple k of itself? (Do not use the function f(x) = 0.)



    2. Relevant equations

    The previous question asked what function was a derivative of itself - with the pretty easy answer of e^x. But I'm stuck on this one.


    3. The attempt at a solution

    To figure it out would involve finding the solution to something like:

    y' = ky

    Or at least that's the answer to the follow up question, which asks what differential equation this would satisfy. So it's something I just need to know.

    I think I'm missing something very simple. I looked through all my calculus material and am at a loss to find such a function, though I have a feeling it's easier than I'm making it.

    -Dave K
     
  2. jcsd
  3. Aug 30, 2012 #2
    1. ekx
    derivative is k.ekx
     
  4. Aug 30, 2012 #3
    Like I thought... too simple! Thanks!

    -Dave K
     
  5. Aug 31, 2012 #4

    Bacle2

    User Avatar
    Science Advisor

    How about also going from y'=ky

    to y'/y= k, to

    ∫dy/y= ∫ k , etc.
     
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