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Math Help - Newton's law of cooling

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    Exclamation Newton's law of cooling

    Newton's law of cooling leads to a mathematical model of the cooling of a hot cup of coffee. The temperature of the coffee at any time is given by the solution of the following differential equation




    Find the general solution of the differential equation

    Find the particular solution of the differential equation if initially, the temperature of the coffee is 83 degrees.

    Find the temperature of the coffee when t = 4.3

    How do I do this?
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    Re: Newton's law of cooling

    \frac{dT}{dt}+ 0.2T- 5= 0 is the same as \frac{dT}{dt}= 5- 0.2T.
    Changing to differential form \frac{dT}{5- 0.2T}= dt. Can you integrate those?
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    Re: Newton's law of cooling

    Quote Originally Posted by leonm92 View Post
    Newton's law of cooling leads to a mathematical model of the cooling of a hot cup of coffee. The temperature of the coffee at any time is given by the solution of the following differential equation




    Find the general solution of the differential equation

    Find the particular solution of the differential equation if initially, the temperature of the coffee is 83 degrees.

    Find the temperature of the coffee when t = 4.3

    How do I do this?
    separation of variables ...

    \frac{dT}{dt} = 5 - 0.2T

    \frac{dT}{dt} = 0.2(25 - T)

    \int \frac{dT}{25-T} = \int 0.2 \, dt

    finish it and get temperature T as a function of time t ...
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    Re: Newton's law of cooling

    to be honest, I haven't got a clue about integrating
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    Re: Newton's law of cooling

    Quote Originally Posted by leonm92 View Post
    to be honest, I haven't got a clue about integrating
    then it's obvious you are ill prepared to tackle this problem ... here is a link for a place to start

    Indefinite Integrals Part 1 | Khan Academy Calculus Lecture
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    Re: Newton's law of cooling

    Quote Originally Posted by leonm92 View Post
    to be honest, I haven't got a clue about integrating
    It is not a good idea to take differential equations until after you have learned calculus.
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