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Math Help - Theoretical Question on Permissable Domains

  1. #1
    Newbie pi_cubed's Avatar
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    Theoretical Question on Permissable Domains

    Hello! Hope this post finds you all well!

    When solving a problem, one may go through step(s) in which the domain
    of the independent variable is restricted. When the final solution of the
    problem is reached, this restriction may not seem to apply. My question
    is if the domain restriction found still applies to the final solution.

    As an example (I apologize for not having learned the typesetting program
    syntax used in this forum - Tex or LaTex?):

    In the linear DE y' + P(x)y = 0, the integrating factor has the form
    exp[integral of P(x)]. I don't remember a specific instance offhand,
    but found that the integrating factor involved the natural logarithm,
    and thus was limited to a domain of x greater than zero. When the
    final solution was reached, there was no restriction on this domain -
    it happened that the domain was the entire x-axis.

    Would the final solution still have the valid domain of x > 0 since the
    integrating factor had that restriction?

    Thanks!

    Phill.

    expression mark-up language yet
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  2. #2
    Newbie pi_cubed's Avatar
    Joined
    Dec 2008
    From
    Redlands, California
    Posts
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    {Correction to Previous Post}

    Hello Again!

    [Oops! - who's tired?]

    Please ignore bad editting fragment at end of post :
    "expression mark-up language yet".

    Thanks!
    Phill.
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