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Homework Help: Simple Diff. Eq.

  1. Aug 29, 2011 #1
    1. The problem statement, all variables and given/known data

    23vda8k.gif

    2. Relevant equations

    you can see my answer in the picture.

    3. The attempt at a solution

    y*e^(-2t) = (-1/2)t*e^(-2t) + (-1/4)e^(-2t) + (1/3)e^(3t) + C
    y = (-1/2)t + (-1/4) + (1/3)e^(5t) + C/(e^(-2t))

    1/3 = 0 - 1/4 + 1/3 + C
    C = 1/4 (i tried 1/4 and -1/4 in the answer box)

    I've even checked my answer by taking the derivative. Where'd I make a simple mistake?
     
  2. jcsd
  3. Aug 29, 2011 #2
    and i tried it with C = 0
     
  4. Aug 29, 2011 #3

    Mark44

    Staff: Mentor

    The only mistake I see is that you forgot to include the homogeneous solution in your answer. You found C = 1/4, which is correct, but your answer doesn't have the e^(2t) term.

    BTW, it's simpler to write e^(2t) than 1/e^(-2t).
     
  5. Aug 29, 2011 #4
    What do you mean by the e^(2t) term?
     
  6. Aug 29, 2011 #5
    Ah, found it. Thanks. Forgot to multiply my C by e^2t
     
  7. Aug 29, 2011 #6

    Mark44

    Staff: Mentor

    The answer you show in the OP is -t/2 + 1/3 *e^(5t) -1/4

    The actual answer (the general solution to the initial value problem) is y = -t/2 + 1/3 *e^(5t) -1/4 + 1/4 *e^(2t)
     
  8. Aug 29, 2011 #7
    Solved.
     
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