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ODE's: IVP Existence/Uniqueness

  1. Feb 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Find a nontrivial solution of the IVP

    dy/dx = tx^p (p is any number); y(0) = 0

    Does this violate the uniqueness part of the Existence/Uniqueness Theorem? Explain


    2. Relevant equations



    3. The attempt at a solution

    I've found two solutions: one for p = 1 and one for all other cases.

    It seems that having two solutions would violate the uniqueness part of the theorem. Both dy/dx and it's partial derivative of y are continuous, so the Theorem can apply, but not sure other than that.

    Any help would be appreciated.
    Thanks
     
    Last edited: Feb 12, 2013
  2. jcsd
  3. Feb 12, 2013 #2

    HallsofIvy

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    No, having different solutions for different values of t does NOT violate the theorem. With different values of p we have different differential equations. But how does 't' come into this equation? Are you sure the left isn't "dx/dt"?
     
  4. Feb 12, 2013 #3

    haruspex

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    Bad post - removed.
     
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