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Understanding uniqueness

  1. Oct 25, 2014 #1

    I was just wondering why taking ∂f/∂y provides the interval on which y is unique (or not necessarily). Could someone possibly provide some mathematical intuition behind this and possibly a proof of some sort detailing why y is unique if ∂f/dy is continuous? Also, how exactly (if it can) is uniqueness determined if ∂f/dy is discontinuous at a certain point?
  2. jcsd
  3. Oct 25, 2014 #2
    I'm confused, what do you mean that "y is unique".
  4. Oct 25, 2014 #3


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    ^Maybe this question is about The[/PLAIN] [Broken] Picard–Lindelöf theorem?

    The theorem gives sufficient conditions so a solution that fails to satisfy the hypothesis might still be unique, but it would need to be shown by a different method. Of course there also might be multiple solutions.

    There should be some discussion of this in most differential equations books.
    Last edited by a moderator: May 7, 2017
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