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Math Help - autonomous equation

  1. #1
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    autonomous equation

    I have the following equation:

    dN/dt = 6- {1/3}N(t), N(0) = 2

    My question is how I should treat N(t). The question is also looking for the equilibrium points. Here's what I did when I treated N(t) as a variable:

    6-1/3N(t)=0
    6= 1/3N(t)
    N(t)= 18

    Am I on the right track?
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  2. #2
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    Hi
    Yes it's the rigth track !

    PS : sorry for my english I'm french ^^

    Solution : N(t)=18+Cexp{-t/3} where C lives in R

    Or N(0)=2 so 2=18+Cexp(-t/3) and you find C
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  3. #3
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    The question also asks to solve the equation. How do I go about doing that?
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  4. #4
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    Quote Originally Posted by jschlarb View Post
    The question also asks to solve the equation. How do I go about doing that?
    It's a linear first order equation. You can always solve these by using an integrating factor.

    -Dan
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