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olive.p

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## Homework Statement

I need help finding the limit of the differential equation.

(dx/dt) = k(a-x)(b-x) that satisfies x(0)=0

assuming

a) 0<a<b and find the limit as t->infinity of X(t)

b) 0<a=b and find the limit as t->infinity of X(t)

## Homework Equations

none

## The Attempt at a Solution

I separated the equation in part a and attempted to solve for x and got a nasty equation

http://www4b.wolframalpha.com/Calculate/MSP/MSP115222ac5cd5fd1ghhf0000016hfg120ch979ad9?MSPStoreType=image/gif&s=20&w=156.&h=41. then I solved for c and found it to be c=-(a/b). I plugged that in for c and got:

http://www4f.wolframalpha.com/Calculate/MSP/MSP49220eh2769a9a2d53700001g9fiib9hd1eh2c3?MSPStoreType=image/gif&s=49&w=159.&h=50. I don't know how to take it further.

I believe that the answer to part a is a based of a graph, but I am unable to prove it.

Thanks in advance.

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