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Math Help - IVP- Uniqueness Theorem and Newton's Law of Cooling

  1. #1
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    IVP- Uniqueness Theorem and Newton's Law of Cooling

    Hi guys,
    I would like some help on these problems please.
    IVP- Uniqueness Theorem and Newton's Law of Cooling-exercise-set-2-question-5.jpgIVP- Uniqueness Theorem and Newton's Law of Cooling-exercise-set-2-question-6.jpg



    I have a quiz soon, which is on this problem set. I can't get help tomorrow as I have classes all day. I have been really busy during the last few weeks on the family farm. I have hired a personal tutor, but we don't start until after the quiz. Thus help would be much much appreciated.I had a read through the uniqueness theorem, but don't really know what to do.

    I'm not exactly sure how to model this.

    Thanks in advance,

    GirandoniAirRifle
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  2. #2
    MHF Contributor

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    Re: IVP- Uniqueness Theorem and Newton's Law of Cooling

    Well, what, exactly, does the "uniqueness theorem" say? In particular, what hypotheses does it have and are they true for this problem?

    For the second, do you know what "Newton's law of cooling" is? It says that the rate at which heat travels from a warmer body to a cooler is proportional to the difference in temperatures. That is, \frac{dT}{dt}= k(T- T_a(t)).
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