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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- May 28th 2011, 02:44 AMZogru11Simple 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 - May 28th 2011, 02:52 AMFernandoRevilla
$\displaystyle y'=C-y\Leftrightarrow \dfrac{dy}{C-y}=dx$ (separated variables) .

- May 28th 2011, 02:54 AMAckbeet
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.

- May 28th 2011, 03:00 AMProve It
$\displaystyle \displaystyle \begin{align*}\frac{dy}{dt} &= C - y \\ \frac{dy}{dt} + y &= C \\ e^{\int{1\,dt}}\,\frac{dy}{dt} + e^{\int{1\,dt}}\,y &= C\,e^{\int{1\,dt}} \\ e^t\,\frac{dy}{dt} + e^t\,y &= C\,e^t \\ \frac{d}{dt}\left(e^t\,y\right) &= C\,e^t \end{align*}$

Can you go from here? - May 28th 2011, 04:20 AMZogru11
No I just didnt realise I was able to do separation of variables :P Thanks for all the answers :)