# Thread: Linear and homogenous, differences...

1. ## 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!

2. "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?

3. 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!

4. You're welcome. Have a good one!