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Should be a simple diff eq but my answer is different than the books

  1. Feb 10, 2009 #1
    1. The problem statement, all variables and given/known data
    dy/dt = 3+e^(-t) - 1/2*y

    2. Relevant equations

    3. The attempt at a solution

    how come i got y = 6e^(1/2t) + 2e^-t - 3

    when the book has y = 6-2e^(-t) - 3e^(-t/2)
  2. jcsd
  3. Feb 10, 2009 #2

    D H

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    Since you didn't show your work, it's a bit tough to know how you arrived at your answer. Show your work, please.

    It is rather easy to verify that your result is incorrect and that the book's is correct. Your result does not satisfy the given differential equation; the book's does. It is a good idea to always double check your work.
  4. Feb 10, 2009 #3

    ok, it's just that it takes me a long time to type all the work, and i've done this problem for > 3 times now

    ok, i'll type up my work haha

  5. Feb 11, 2009 #4
    [itex]1/2y + dy/dt = 3 + e^{-t}[/itex]

    [itex]e^{1t/2}y = 3 (integral)(e^{(1t/2)} + e^{-t}*e^{(1t/2)}[/itex]

    [itex]y = 6e^{(1t/2)}-2e^{(-1t/2)}[/itex]

    that's only the general solution, since i need to get this right in order to figure out the particular solution...

    it's actually (1/2)t, not 1/(2t)..
  6. Feb 11, 2009 #5

    D H

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    Step 2 does not follow from step 3. You dropped a key factor.
  7. Feb 11, 2009 #6
    O LOLzzz

    did i forget about c?

    hahaha .....
  8. Feb 11, 2009 #7

    D H

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    No, you did not forget about c. (Well, you did, but that is not what I was talking about.)

    Look at the left-hand side of your second equation.
  9. Feb 11, 2009 #8

    haha alright, thanks i think i got it
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