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Math Help - Linear and homogenous, differences...

  1. #1
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    Linear and homogenous, differences...

    I was wondering if perhaps someone here could give me a hand sorting out what's what between some different classes of diff. equations:

    My basic understanding of a homogenous diff is that it can be written on a form of the type (for first order)
    y'(x) + p(x)y(x) = 0
    where being equal to zero was of prime concern. Recently though I've understood that this isn't a complete understanding at all. I recently head that the basic definition of a homogenous diff is in fact that you can express a dx/dy as a function of x/y; that is, the variables scale. And then you have the option of solving using a variable substitution, x/y = v for example.

    So yea, currently I'm feeling a little bit lost in between linear, homogenous and linear homogenous. If anyone feel like giving a bit of an explanation, or perhaps link to some good source of disambiguation, as it were, I'd be very grateful!
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  2. #2
    A Plied Mathematician
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    "Homogeneous" can mean either that there are no terms that do not contain y or one of its derivatives, or it can mean that the coefficients of all differentials are homogeneous functions of the same degree, depending on the context. Why not take a look at Chris's DE Tutorial?
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  3. #3
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    Actually, that one line was exactly what I needed to click things into place; just a clear cut sum-up of when the term homogenous is applicable. Thanks a lot!
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  4. #4
    A Plied Mathematician
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    You're welcome. Have a good one!
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