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Solution of an Ordinary Differential Equation

  1. Oct 22, 2013 #1
    Hi,

    The definition (see attachment) says that f(x) is a solution to
    the differential equation if it satisfies the equation for every x
    in the interval.

    Assuming that I have a differential equation that I want to
    solve and the D.E. has an interval [itex]I_1[/itex], and I've
    come up a solution with an interval [itex]I_2[/itex],
    where [itex]I_2[/itex] is a subset of [itex]I_1[/itex], is it
    still a solution to the differential equation? If it isn't, does the
    solution still make sense?

    I'm new to differential equations and haven't solved anything
    DE yet.
     

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  2. jcsd
  3. Oct 22, 2013 #2

    BTP

    User Avatar

    The blurb could be a little bit clearer. When talking about a solution to a differential equation in a given problem the domain of interest is essential. The blurb implies this but it could be explained a bit more explicitly. So to answer your question, it is not a solution to a specific problem posed on [itex]I_1[/itex]. That you found a function that works on [itex]I_2[/itex] would satisfies a different problem, one posed on [itex]I_2[/itex].
     
    Last edited: Oct 22, 2013
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