I need help finding the limit of the differential equation.
(dx/dt) = k(a-x)(b-x) that satisfies x(0)=0
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)
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. [Broken] 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. [Broken] 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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