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February 6th, 2017, 07:38 AM   #1
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Differential help

Hi there! I am trying to write a project to model the spread of rumours and have reached a step involving proving an integration in a differential. Could anyone help to give a value for S?
dS/dt=kS(M-S) where k and M are constants
Thanks in advance!
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February 6th, 2017, 08:03 AM   #2
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dS/dt=kS(M-S) where k and M are constants
separate variables ...

$\dfrac{dS}{S(M-S)} = k \, dt$

partial fraction decomposition ...

$\displaystyle \int \bigg[\dfrac{1}{S} + \dfrac{1}{M-S}\bigg] \, dS = \int kM \, dt$

Solve for $S$ from this step? $S(t)$ will be a logistic function ...
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