How to you find the general solution of $(dr)/(ds)=0.05r$ ?

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Answer 1 · 2017-05-24T08:06:26

$r = Ae^(0.05s)$

We have:

$(dr)/(ds)=0.05r$

Which is a First Order linear separable DE. We can simply separate the variables to get

$int \ 1/r \ dr = int \ 0.05 \ ds$

Then integrating gives:

$\ \ ln | r | = 0.05s + C$
$:. | r | = e^(0.05s + C)$
$:. | r | = e^(0.05s) *e^C$

And as $e^x >0 AA x in RR$ , and putting $A=e^C$ we can write the solution as:

$r = Ae^(0.05s)$

How to you find the general solution of (dr)/(ds)=0.05r(dr)/(ds)=0.05r?