# How to rearrange DE?

• Aug 3rd 2010, 01:09 AM
wazz
How to rearrange DE?
Would really appreciate any ideas on rearranging this DE into a form that is ready to be solved using either separating of variables or integrating factor method.

dn/dt= r(1-n/s)n,

Where r and s are constants.

Any help would be appreciated
• Aug 3rd 2010, 01:14 AM
Prove It
$\frac{dn}{dt} = r\left(1 - \frac{n}{s}\right)n$

$\frac{dt}{dn} = \frac{1}{r\left(1 - \frac{n}{s}\right)n}$

$t = \int{\frac{1}{r\left(1 - \frac{n}{s}\right)n}\,dn}$.

Now apply the method of Partial Fractions.