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Help finding the function

  1. Nov 29, 2011 #1
    I have

    (θ[itex]_{1}[/itex]-θ[itex]_{2}[/itex])*exp(r*t) + r* Y = dY/dt

    How can I find Y?
    I tried to reverse the f ' g +g' f but I keep getting an extra term

    Thanks
     
  2. jcsd
  3. Nov 29, 2011 #2

    LCKurtz

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    Write it as
    [tex]y' - ry = (\theta_1-\theta_2)e^{rt}[/tex] Multiply both sides by e-rt and you should have an exact derivative on the left side.
     
  4. Nov 29, 2011 #3
    Couldn't quite get it? What do you mean by exact derivative?

    so what is y?
     
  5. Nov 29, 2011 #4

    LCKurtz

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    Show us what happened when you followed my advice. The left side should look like the derivative of a product. What did you get?
     
  6. Nov 29, 2011 #5
    so we have:

    exp(-r*t) y' - exp(-r*t) r y = theta1 - theta2

    I assume you mean
    f = exp(-r*t)
    g = y

    but I'm not sure how to place thetas

    so I think y will have a exp(r*t) in it but not sure about the rest.
     
    Last edited: Nov 29, 2011
  7. Nov 29, 2011 #6

    LCKurtz

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    Yes, so the left side is (e-rty)' so your equation is: [tex](e^{-rt}y)'=\theta_1-\theta_2[/tex] I assume the thetas are constant. So what do you get when you integrate both sides with respect to t and solve for y?
     
  8. Nov 30, 2011 #7
    Yep, got it.

    Thanks
     
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