Differential Equations:
A disease is introduced into a community of 5000 individuals. If the rate at which the disease spreads through the community is jointly proportional to the number of people who have the disease and the number of individuals who have not caught it, write down the differential equation for the number of people, x(t) who have caught the disease by time t.

Question

Differential Equations: 
A disease is introduced into a community of 5000 individuals. If the rate at which the disease spreads through the community is jointly proportional to the number of people who have the disease and the number of individuals who have not caught it, write down the differential equation for the number of people, x(t) who have caught the disease by time t.

radar · Answer

x=(t)(5000-t)
x=5000t-t^2
x(t) = 5000-2t

radar · Answer

Maybe it is more complicated than that, but that's my wag.

s · Answer

Thank you!

Well, I'm not sure either.. i thought a constant of proportionality k would be involved.. also i think it has to start with y'=.. because it says write a differential equation.. but i still don't know how to put it in one whole differential equation..