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An oddly puzzling differential equation

  1. Sep 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve t*y'(t) + 4*y = 0; y(3) = 2. This is the solution---> Ans: y(t) = 162t^(-4)





    2. Relevant equations
    I need to know how my professor got this answer.


    3. The attempt at a solution
    I attempted by subtracting 4y to the other side and separated the variables to yield
    [tex]\int(dy/y)[/tex] = -4[tex]\int(dt/t)[/tex]
    for which you get ln(y) = -4ln(t)
    => y = t*e^(-4).
    Can anyone help me on this?
    (I left out the constant of integration since that only pertains to part 2 for a particular solution)
     
  2. jcsd
  3. Sep 10, 2009 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    Are you sure you applied your exponent/logarithm rules correctly?

    By the way, the constant of integration is always relevant. Forgetting it is in the same class of mistakes as forgetting that -2 is a solution to x²=4.
     
  4. Sep 10, 2009 #3

    lanedance

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    Homework Helper

    have a look at your exponent step

    ln(y) = -4ln(t)
    now take exponential
    eln(y) = y = e-4ln(t)

    note - e-4.eln(t)= e-4 + ln(t), not what you have...
     
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