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December 17th, 2009, 03:46 AM   #1
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ODE 1

I've attached the relevant pictures. The question is:
Let X,Y be two containers.
At t=0, container X has 100 lt. of water with 2 kg of salt in it and Y has 100 lt. of water with 6 kg of salt.
On each t>0, the system transports water as the you can see in the picture.

In each minute t, let x(t), y(t) be the quantities of salt in X,Y in kg's.
t is measured in minutes!

You should notice that on each time, there are exactly 100 lt. in each container!

Write an ODE that gives the quantity of salt in each container as a function of time, solve it and calculate how much kg's of salt will be in the container after 10 minutes from the start of the process.
My attempt:

I wrote the equations this way:
x'(t)= -8x(t)/100 +2y(t)/100
y'(t) = 8x(t)/100 -8y(t)/100

We get the ODE: w' =Aw ... The eigenvalues of A are: -4/100 and -12/100 ...
After I solve these two equations, I get two solutions - one for x(t) and one for y(t)... The only problem is that these solutions don't match the data of the question...
HELP is needed!

TNX
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File Type: jpg ODE1.JPG (39.9 KB, 93 views)
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December 17th, 2009, 07:35 PM   #2
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Double the first of your two equations, then their sum and difference are equations you can solve immediately.
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