## How to solve this differential equation? [closed]

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?

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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
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
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