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Math Help - Uniqueness Theorem

  1. #1
    Member
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    Uniqueness Theorem

    Hi all,

    I have the following D.E.

    \frac{dy}{dt} = \sqrt{y^2+1},\\ y(t_0) = y_0

    How can i find a value of y_0 and a value of t_0 such that there is a unique solution to the initial-value problem?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    The functions

    f(t,y)=\sqrt{y^2+1},\;\;\dfrac{\partial f}{\partial y}

    are continuous on \mathbb{R}^2 , so for every (t_0,y_0)\in \mathbb{R}^2 there exists a unique solution satisfying y(t_0)=y_0 .
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