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Math Help - Simple first order diff. eq

  1. #1
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    Simple first order diff. eq

    Hi! I have a simple question that i cant get thorugh at the moment. I have a differential equatoin of the form:

    y' = C - y

    where y' = dy/dt

    How can I solve this. I cant do separation of variables here. Help plz
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    y'=C-y\Leftrightarrow \dfrac{dy}{C-y}=dx (separated variables) .
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  3. #3
    A Plied Mathematician
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    Do you mean you aren't allowed to do separation of variables? Or that you don't think separation of variables will work for this problem? Because you can do separation of variables. You could also do an integrating factor if you wanted. And probably a few other techniques as well.
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  4. #4
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    Quote Originally Posted by Zogru11 View Post
    Hi! I have a simple question that i cant get thorugh at the moment. I have a differential equatoin of the form:

    y' = C - y

    where y' = dy/dt

    How can I solve this. I cant do separation of variables here. Help plz
    \displaystyle \begin{align*}\frac{dy}{dt} &= C - y \\ \frac{dy}{dt} + y &= C \\ e^{\int{1\,dt}}\,\frac{dy}{dt} + e^{\int{1\,dt}}\,y &= C\,e^{\int{1\,dt}} \\ e^t\,\frac{dy}{dt} + e^t\,y &= C\,e^t \\ \frac{d}{dt}\left(e^t\,y\right) &= C\,e^t \end{align*}

    Can you go from here?
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  5. #5
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    No I just didnt realise I was able to do separation of variables :P Thanks for all the answers
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