Talk:Differential equation

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Differential equation is included in the 2006 Wikipedia CD Selection, or is a candidate for inclusion in the next version. Please maintain high quality standards and, if possible, stick to GFDL-compatible images.

This article is within the scope of WikiProject Mathematics.
Mathematics grading:	Start Class	Top Importance	Field: Analysis
A vital article
needs expansion.

Old talk moved (along with page) to Talk:Ordinary differential equation. -- Walt Pohl 20:54, 23 Jan 2005 (UTC)

Contents 1 Text copied for keywords 2 Removing reference 3 Vote for new external link 4 Intended audience 5 Linearity 6 About the Image 7 Made a new graph

[edit] Text copied for keywords

Hello. I understand that other sites can use information from this site, and my site is a free information sharing wiki also. I've copied the main text of this front page and put it in a comment in my web site template (www.exampleproblems.com link), because it has lots of keywords and math phrases. I hope that is ok. -thanks -Tbsmith

[edit] Removing reference

I removed a reference that seems to have been added for no other reason than to allow a link to the bookseller's page. The reference was added by someone who doesn't seem to have contributed to the article in any way; and the same reference was added to Ordinary differential equation by the same person (who doesn't seem to have contributed to that article, either). The reference doesn't seem to be well known or widely available, and I find it quite doubtful that it was used at all in writing or editing this article, or used meaningfully in fact-checking. In anyone objects to this removal, please discuss here. - Ruakh 22:53, 13 August 2005 (UTC)

[edit] Vote for new external link

Here is my site with differential equations example problems. Someone please put this link in the external links section if you think it's helpful and relevant. Tbsmith

http://www.exampleproblems.com/wiki/index.php?title=Ordinary_Differential_Equations

[edit] Intended audience

"In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables"

Who is this article aimed at? Seems to be another mathematics article that is written by a mathematician for another mathematician of the same level of knowledge. If differential equations require a certain level of knowledge of mathematics to be understood then this would be nice to be indicated on the page.

[edit] Linearity

"A differential equation is linear if it involves the unknown function and its derivatives only to the first power; otherwise the differential equation is nonlinear."

I am not sure this is the correct definition. What about eqn's such as |dy/dx| + |y| = x? Isn't this non linear. (Here |.| is the modulus function.) What about y(dy/dx) = x. I though linear equations were defined as those which are of the form: Ay^(n) + By^(n-1) + ... Cy + D = 0 where A,B,...,C,D are functions of x. Not sure how this classifies a PDE. Can someone please clarify?

Your definition is indeed the correct one, and works fine for ODEs. PDEs linearity is analogous, though for a better understanding of linearity one should consider that a ODE or a PDE can both be written as Pf=g where f and g are suitable functions on R^n and P is a differential operator. Evaluating the linearity of both is actually testing the linearity of the differential operator.

(Antonius Block 23:39, 27 November 2006 (UTC))

[edit] About the Image

The caption reads

An illustration of a differential equation. The arrows show how the differential equation locally influences a state, while the lines display how specific solutions are determined by starting conditions (red dots).

I agree to the point of red dots and their relation to initial conditions. But what is meant by the arrows show how the differential equation locally influences a state??? To my knowledge these lines are the so-called integral curves and the arrows define the direction field of that particular differential equation which is used to solve that equation approximately by plotting several integral curves. This method is called isocline or isoclyne or whaterver (sorry I don't know maths terminology in English very well).

Am I right? If that is the case, could someone please correct the caption? RokasT 19:16, 9 January 2007 (UTC)

The image is gone as it was copyvio. Can someone make a new image? User A1 05:55, 2 February 2007 (UTC)

It's not clear to me why the image was deleted. I asked the person responsible for clarification at commons:User talk:Bryan. -- Jitse Niesen (talk) 06:59, 2 February 2007 (UTC)

I asked for it to be deleted (on IRC, didn't know how to delete stuff from commons) because its the direct rip of the samples provided with apples grapher application, no actual work has been done other than "print screen". see User talk:Romansanders User A1 07:35, 2 February 2007 (UTC)

[edit] Made a new graph

Hello,

I made a new image for this article

as I was responsible for the deletion of the other image (due to copyright issues) i felt i should replace it with an image with a clearer licence. Can someone add this to the article? Thanks User A1 05:48, 24 February 2007 (UTC)

Sure, I'll add it in... thanks a lot!!, and feel free to contribute more.. this article doesn't seem to do justice to the topic. Danski14 16:21, 24 February 2007 (UTC)