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Thread: Forst order linear ordiny differential equation

  1. #1
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    Question Forst order linear ordiny differential equation

    Hei!

    Can anyone help me to give an excatly explanation/translation of the following differential equations:
    1. T'(t)=-k .(T_(t)-T_(r)) where T_r is a constant

    2. y"_(t)=-10

    Thanx
    Last edited by Haytham1111; May 21st 2017 at 07:11 AM.
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  2. #2
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    Re: Forst order linear ordiny differential equation

    Quote Originally Posted by Haytham1111 View Post
    Hei!

    Can anyone help me to give an excatly explanation/translation of the following differential equations:
    1. T'(t)=-k .(T_(t)-T_(r)) where T_r is a constant

    2. y"_(t)=-10

    Thanx
    #1 looks like the DE for Newton's Law of Cooling ...

    $\dfrac{dT}{dt} = -k(T - T_r)$, where $T_r$ is the ambient temperature surrounding an object that has temperature $T$ as a function of time.

    The rate of change of temperature of an object is directly proportional to the difference between the object's temperature and its surroundings.


    #2 looks like the approximation of acceleration due to gravity near the Earth's surface ...

    $a = \dfrac{dv}{dt} = \dfrac{d^2y}{dt^2} = -10 \, m/s^2$

    The rate of change of an object's velocity in free-fall (in the absence of air resistance) is a constant.
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