I have a logistic issue with differential equations. I have spent four hours working on this problem and it is way past the point of ridiculous.(adsbygoogle = window.adsbygoogle || []).push({});

If anyone can help out that would be great.

It begins like this.

dy/dt = k(P-y)*y. It is an epidemic model, where k is a positive constant relating the rate of infection. P is total population involved. An initial condition of y(0)=t is given. I am to find this particular solution.

The y is multiplied. Strange that it isnt shown as ky(p-y) but perhaps its a hint that im not getting.

Anyway, I am treating this as a separable equation as that is the tool we are given (the method).

I have tried numerous approaches and have gotten the farthest with this one.

dy/(y(p-y)= kdt

Partial fractions on the left side where A and B are both = to 1/p.

1/py + 1/(p(p-y)) dy = kdt

Then integrate both sides.

ln(y)/p - ln(p-y)/p = kt + c.

Here is where the problem begins (unless I screwed up earlier). A CAS gives me -ln(y-p) (second term left side) . Can anyone explain this? I integrated by U substitution. Why would the variable and constant be switched?

I continued on assuming the CAS was correct and now I cannot isolate Y variable. I have never had this trouble before with math but hey I guess thats the way it goes.

Any help would be greatly appreciated.

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# Homework Help: Diff Eq. Epidemic model.

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