Simple first order diff. eq

**Zogru11** · May 28th 2011, 02:44 AM

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

**FernandoRevilla** · May 28th 2011, 02:52 AM

$y'=C-y\Leftrightarrow \dfrac{dy}{C-y}=dx$ (separated variables) .

**Ackbeet** · May 28th 2011, 02:54 AM

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.

**Prove It** · May 28th 2011, 03:00 AM

Originally Posted by Zogru11

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?

**Zogru11** · May 28th 2011, 04:20 AM

No I just didnt realise I was able to do separation of variables :P Thanks for all the answers

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