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February 6th, 2017, 08:38 AM  #1 
Newbie Joined: Feb 2017 From: London Posts: 1 Thanks: 0  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(MS) where k and M are constants Thanks in advance! 
February 6th, 2017, 09:03 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,290 Thanks: 1120  Quote:
$\dfrac{dS}{S(MS)} = k \, dt$ partial fraction decomposition ... $\displaystyle \int \bigg[\dfrac{1}{S} + \dfrac{1}{MS}\bigg] \, dS = \int kM \, dt$ Solve for $S$ from this step? $S(t)$ will be a logistic function ...  

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