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Can I separate a differential equation?

  1. May 16, 2013 #1
    Given the following differential equation

    x*x''+(x')^2+y*y''+(y')^2=C

    where C is a constant and all differentiation is with respect to time


    Can i equal the first and second parts of the equation into different constants and solve separately?, meaning solving the system

    x*x''+(x')^2=k^2
    y*y''+(y')^2=C-k^2
     
  2. jcsd
  3. May 16, 2013 #2
    No. Why would you expect that to hold true?
    The equation can be slightly simplified though.
    Think of how ##x x'' + (x')^2## can be rewritten.
     
  4. May 16, 2013 #3
    You can write it has first order equations but I don't know if that is your aim.
     
  5. May 17, 2013 #4

    vela

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    [STRIKE]Yes. Why do you suppose you can do that?[/STRIKE] (Never mind.)
     
    Last edited: May 17, 2013
  6. May 17, 2013 #5

    LCKurtz

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    I don't see why the constant must be positive for the ##x## equation. But, more to the point, I am unconvinced that the answer is yes. It isn't like the eigenvalue situation you get in separation of variables in partial DE's because the two sides have different independent variables. Or maybe that isn't what your reasoning is.
     
  7. May 17, 2013 #6

    Mark44

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    I like this idea.
     
  8. May 17, 2013 #7

    vela

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    Yeah, you're right. Never mind my earlier post.
     
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