Wikipedia:Reference desk archive/Mathematics/2006 August 27
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Linear Differential Equation
I know how to solve linear differential equations, but the y3 on the right side has totally confused me. Here y=y(x).--Patchouli 08:57, 27 August 2006 (UTC)
- See the section "Linear differential equations with variable coefficients" on Linear differential equation. That has the method for solving such a DE. Dysprosia 09:03, 27 August 2006 (UTC)
- I had looked at that already. It doesn't help me eliminate y3.--Patchouli 09:07, 27 August 2006 (UTC)
- Oh, whoops. Dysprosia 11:37, 27 August 2006 (UTC)
- You should have directed me to Bernoulli differential equation.
Integrating factor is .
--Patchouli 09:38, 27 August 2006 (UTC)
- While that method works here, so does separation of variables, which in this case is quite easy:
- --LambiamTalk 10:31, 27 August 2006 (UTC)
- I wasn't thinking of partial fractions for integrating::.
Your solution is imaginative.--Patchouli 11:03, 27 August 2006 (UTC)
I was recently reading a (non-WP) article that uses the notation with and k an integer to denote some sort of continuity. The paper failed to describe the meaning of this notation. From the context, it was clear that it was kind-of-like viz. the set of k-times differentiable functions. For a while, I thought this might refer to Sobolev space, but the condition makes this seem unlikely. Any hints about what this notation might be? FWIW, this is a survey article, so the author was clearly assuming that this is a basic notation. FWIW, this is the article: Potential theory, the notation shows up just a little more than 1/3 of the way in. Its mostly just plain-old stock, ordinary integrals and derivatives on plain-old flat space, nothing fancy, nothing topological, or otherwise whiz-bang, nothing beyond multivariate calculus. linas 15:31, 27 August 2006 (UTC)
- Could it be functions with Holder continuous k-th derivative? See Holder condition (Igny 16:16, 27 August 2006 (UTC))
- Why yes, of course, that's exactly it. Thanks. linas 03:05, 28 August 2006 (UTC)