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Order of a Differential Equation

  1. Jun 12, 2010 #1
    Hi. I'm reading a differential equation book to prime myself best for my signals and systems class I'm in, and I've ran into some confusion.

    If I had a differential equation like so:

    [tex]y'(t) + \int y(t)dt = f(t)[/tex] (1)

    What would you say the order is? The definition says "the order of a differential equation is the highest derivative that appears in the equation."

    Would I say it's a second order differential equation because:

    [tex] h(t) = \int y(t)dt[/tex] (2)
    meaning:
    [tex] h''(t) = y'(t)[/tex] (3)
    and substituting (2) and (3) into (1):
    [tex]h''(t) + h(t) = f(t)[/tex] (4)

    If asked to solve such a differential equation, would I first solve (4) and then differentiate h(t) to find y(t), the original function of t in question?
     
    Last edited: Jun 12, 2010
  2. jcsd
  3. Jun 12, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    What you have initially is NOT a "differential equation". It is an "integra-differential equation" and the term "order" does not apply to it. Assuming f(t) is some reasonable function, then yes, the method you describe for solving it should work.
     
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