Order of a Differential Equation

  • Thread starter debrox
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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?
 
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Answers and Replies

  • #2
HallsofIvy
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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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