0

I want to solve this differential equation:

$$ C \cdot y(t)\frac{d}{dt} = x(t) - y(t) $$

$x(t)$ and $y(t)$ are two ordinary functions of t, C is a constant - all in in $R$

I am trying to solve it towards $y(t)$. The solution I am looking for looks something like this:

$$ y(t) = e^{\int{x(t)dt}} + C $$

So $\int{x(t)dt}$ can stay - but how will the rest look like and could you show me the individual steps and name the method how to solve it? Could "variation of the parameters" be applied?

flag
This comes very close to what I'm trying to do but my equation is a little bit simpler: de.wikipedia.org/wiki/Variation_der_Konstanten – NW Patrick Jun 23 2011 at 21:07
5 
 Sorry but, $d/dt$ is applied to what? – shenghao Jun 23 2011 at 21:19
And definitely not functional analysis. – András Bátkai Jun 23 2011 at 22:16
2 
 The first step would be to write it properly. But this is from a first course in differential equations, so does not belong in this web site. See our FAQ for reasons why, and where to post instead. – Gerald Edgar Jun 23 2011 at 22:48
$\frac{d}{dt}$ is applied to $t$, which $y(t)$ is a function of. I thought I knew what a differential equation is. @Gerald There are of course (many) other possibilities to write it down. Which notation would you prefer ? – NW Patrick Jun 24 2011 at 14:13

closed as too localized by Gerald Edgar, fedja, Andres Caicedo, Will Jagy, Willie Wong Jun 24 2011 at 2:06

Browse other questions tagged or ask your own question.