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Mathematica (diffeq) - solving a function inside of a diffeq in terms of another function

dilligent
dilligent asked
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Last Modified: 2012-05-11
Hello,  I've been scratching my head on a particular question for hours now, and it's pretty clear that I need help.  I have a diffeq:

y'[t]==d[t] (40-y[t])+0.5 (o[t]-y[t])
y[0]==starter



, and I am supposed to come up with a function d[t] expressed in terms of o[t] so that the solutions of y[t] of the function diffeq above settle in at about 50.  How would I go about doing this?  I've tried separation of variables and DSolve to no avail.  Any ideas?  I need a good explanation more than just the answer.  Thanks!  o[t], incidentally, equals 80-11 Cos[[Pi t)/12]+3.25691 Sin[Pi t/12]
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Sorry, this actually was related to what the expert posted.  I need to credit him.

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Would you like to post the steps to your solution for review. I think I got a different answer than you (but maybe not, since your answer uses different symbols than in your OP). For example, you final answer began with c[t_]= ...
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