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May 28th, 2007, 10:15 AM   #1
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Differential equation

Hi, I need a little help on this problem.

I am asked to find the equilibrium solution to this DE:

y' = e^(-t) + y

If I set y' to zero, I get 0 = e^(-t) + y

then...

-y = e^(-t)
ln|-y| = -t

Is this correct?
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May 29th, 2007, 01:54 AM   #2
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The equation you gave has solution y = c e^t - ½ e^(-t).

There is no equilibrium solution in the usual sense of equilibrium. Can you explain what was meant by "equilibrium solution" in this question?
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May 29th, 2007, 06:26 PM   #3
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Well, I need to draw a slope field for this differential equation and assumedd that it will have an equilibrium solution that either diverges or converges.
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