Talk:Differential equation

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

Flow

This article flows poorly. Obstructive clauses abound. There is also a decent amount of unnecessary language. I am going to attempt to fix it in a series of small edits so they can be reviewed. Would someone please double check what I do? I don't want to delete something important or add any mistakes of my own. — Preceding unsigned comment added by 70.127.17.241 (talk) 13:48, 3 March 2020 (UTC)

remove ODE table

That table is quite useful to have, but its only on ODE's and should be moved to that article, also the nomenclature should be more standard (I'm in the process of rewriting that article).F = q(E+v×B) ⇄ ∑_ic_i 10:02, 23 May 2012 (UTC)

Blend/remove classification summary and nomenclature sections

The section Ordinary DE classification is already contained in Ordinary differential equation and places too much emphasis on ODEs for this article, which should balance PDEs and ODEs. I am going to remove most of that section (especially deleting the table) and modify the more general section Nomenclature to compensate. F = q(E+v×B) ⇄ ∑_ic_i 07:08, 18 June 2012 (UTC)

this article is unclear, i made this edit -- http://en.wiki.x.io/w/index.php?title=Differential_equation&diff=516518566&oldid=516434444

this article is unclear, i made this edit -- http://en.wiki.x.io/w/index.php?title=Differential_equation&diff=516518566&oldid=516434444 — Preceding unsigned comment added by Coginsys (talk • contribs) 10:35, 8 October 2012 (UTC)

article is unreadable

this article needs to improve, it's really unreadable. it's unclear. you need to make it understandable to non-experts,

the lead should say what differential equation does. what it is used for and what it finds out. ALL ARTICLES SHOULD BE DOING THIS IN THE FIRST SENTENCE

that's just one example, i'll add more after the first problem is cleared up

see http://en.wiki.x.io/wiki/Wikipedia:Make_technical_articles_understandable if you need help — Preceding unsigned comment added by Coginsys (talk • contribs)

In my reading, the lead does say (in the second and third paragraph) what a differential equation is used for. Do you think those paragraphs can be improved (and if so, how), or are you concerned about something else? I don't see what part of Wikipedia:Make technical articles understandable you are refering to. -- Jitse Niesen (talk) 09:19, 12 October 2012 (UTC)

list of problems in the lead

im not sure why it doesn't come earlier. the 5ws includes who, what, etc.

and some of these articles just has who in the first sentence or 2, all articles should at least have who and what.

anyway, i'll break it down for anyone who likes to make readable articles on wikipedia:

breaking down the lead

Differential equations arise in many areas of science and technology,

- this is fluff and repetitive of the last part of the first paragraph

specifically whenever a deterministic relation involving some continuously varying quantities

- ok...

(modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated.

- it just gets more and more abstract AND this sentence is WAY TOO LONG. are those even allowed on the MOS...

This is illustrated in classical mechanics, 

- yawns, i dont understand why some of articles are so dragged out and never get to the point0

where the motion of a body

- what body? do you mean object? like a boat? or any physical "object" -- does body specifically refer to physically bodies or what? does it include digital objects? this is very very unclear

is described by its position and velocity as the time value varies.

- what time value? what is this referring to? to the independent variable or the dependent one? where is this coming from? something said earlier? or frrom nowhere?

Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body) 

- is this implying that differential equation is ONLY for physical objects? because differential equation is applied to lots of different things. why it classical mechanics being used as an example? and only that? this is undue weight. this is also doesnt seem to be a really good example

to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly

- so what is this trying to find? what does differential equation finding? is it finding where the ball will land exactly? or the radius where the ball will land?

if so, is that the only thing differential equation does?

if so, it's made incrediably complex.

if not, then is it finding how fast the ball will go?

if so, does it average out the speed of the ball?

if not, then is it finding how fast the ball will go every second?

or does it find the change between the speed of the ball in the current second compared with the previous second?.

- ok, i think i'll stop here...

An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation.

Coginsys (talk)

very important example of what is good

look at the changes on http://en.wiki.x.io/w/index.php?title=Time_series&diff=518032407&oldid=516614772

someone actually made it better

"In the context of... the primary goal of time series analysis is forecasting"

...it is used for signal detection and estimation

can be used for clustering, classification, query by content, anomaly detection as well as forecasting

and they added important and significant sections

the article was just trash orginally and nobody was improving it

and then when you edit something, ppl dont improve it, all they do is change it back to the trash it was

Coginsys (talk) —Preceding undated comment added 07:51, 16 October 2012 (UTC)

I'm not sure how to deal with these problems, but here goes nothing.

A differential equation is, quite frankly, a technical thing, and a non-specialist can't seriously hope to understand the whole business by reading a Wikipedia article. If one of you folks is a good writer (but might not know the mathematics, but is on board with the objective of making a stab at an introduction for the layman,) here's something you might be able to use.

"In the mathematical treatment of the exact sciences, mathematical quantities are assigned symbolic variables, such as 't' for time, 'x, y, z' for position coordinates, 'm' for mass, and so on. Calculus is the study of the rates at which some of these variables change relative to the others. In the course of expressing a law, equations arise which contain both the variables themselves, and their rates of change, and it is these that are called 'differential equations.' The task that the subject of Differential Equations sets itself is broadly to understand the meaning of a differential equation in terms of the geometry that underlies it, and to discover, if possible, simpler equations with fewer of those rates of change (or 'derivatives', as they are called). In particular, if it possible, it is desired to obtain an equation with no rates of change (derivatives) at all."

The unreadability of the article arises not for want of effort, but by the nature of the material. The general suggestion to keep only the most qualitative descriptions of the problems and the approaches here, and move all procedural and specific material to other specialized pages is the only approach that will work. (Look in Brittanica, 1974. The problem was not solved there, either.) — Preceding unsigned comment added by Arch5280 (talk • contribs) 21:22, 13 January 2014 (UTC)

Is the class of solutions always a set?

The article says: "solutions —the set of functions that satisfy the equation" but is the class of solutions really always a set? — Preceding unsigned comment added by 213.10.46.38 (talk) 15:30, 11 April 2013 (UTC)

What is the problem? The class of all functions from a given set to a given set is a set; and every its subclass is. Boris Tsirelson (talk) 19:12, 11 April 2013 (UTC)

Add real-world grounding to the Examples

The Examples give formulas, but no indication of what real-world problems they relate to. A non-expert might well be helped by knowing that a particular formula describes behaviors that they already know about in a non-mathematical context. — Preceding unsigned comment added by RichMorin (talk • contribs) 05:41, 30 May 2013 (UTC)

Seconded. As the it currently stands, the casual reader (such as myself) ends up with 42 browser tabs open with all the fancy math nerd terms used. Since those pages then reference other terms, the cycle is endless. An article this high on the list of frequently referenced math subjects should illustrate - with visuals and/or English - why exactly a differential equation is a differential equation, and show at least one example with a complete description of usage in a real-world scenario that can be followed with natural human intuition. Krushia (talk) 14:11, 12 December 2013 (UTC)

'Nuther Inane Intrusion by a Wikipedia Editor

As is too often the case, a perfectly sensible Wikipedia entry comes littered with colourful boxes sprinkled about by nit-wit editors.

The article has one of the funnier ones. Before we get to the article at all we have a screenfull of edi-boxes, of which the first begins "This article or section lacks a single coherent topic."

One cannot help but be reminded of Will Rogers's "I am a member of no organized political party. I am a Democrat."

Homeomorphically here, the article has no coherent topic. It is about differential equations.

David Lloyd-Jones (talk) 05:13, 12 January 2014 (UTC)

Two of them were added by a drive-by editor without any explanation. I removed them. -- Jitse Niesen (talk) 08:31, 14 January 2014 (UTC)

Actually, the editor did somewhat explain his reasoning when he added those tags (diff), but it is easy to miss. — Tobias Bergemann (talk) 11:16, 14 January 2014 (UTC)

I stand corrected. No idea how I could have missed that. -- Jitse Niesen (talk) 13:57, 14 January 2014 (UTC)

Sections could benefit by adding images

More images helping to explain concepts or provide examples/representations would be nice.

Differential Equations is an extremely rich field, but this wall of text does not do it justice. Even as a physicist, I am not engaged by this article... Now how interested do think an average teenager would be?

Here are some ideas: talk about analytically tractable vs. intractable DEs, with imagery illuminating both. Perhaps a lorenz attractor for the latter https://moodle.insa-toulouse.fr/pluginfile.php/35347/mod_label/intro/LorenzAttractor.png — Preceding unsigned comment added by Rablankenship (talk • contribs) 02:54, 14 September 2014 (UTC)

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The section on physics

The section of physics

Could anyone write down the specific equation, rather than list the title or the name of the equation? — Preceding unsigned comment added by 130.199.3.165 (talk) 19:06, 26 January 2016

Nonlinear differential equation redirect page

This page redirects to Nonlinear_system#Nonlinear_differential_equations instead of Differential_equation#Non-linear_differential_equations. Is this an error? Jarble (talk) 05:10, 21 June 2018 (UTC)

I think it’s an error and should be changed. Dolphin (t) 07:15, 21 June 2018 (UTC)

Is there such a thing as the "Sagnik's equation?"

This article mentions "the Sagnik's equation", but I can't find any mentions of this equation online. Does this equation actually exist? Jarble (talk) 05:54, 20 November 2018 (UTC)

I have never heard of this. I am going to remove that redlink. – Tea2min (talk) 12:20, 20 November 2018 (UTC)

Definition of Differential Equation is not correct

@D.Lazard: The current definition of Differential Equation "a mathematical equation that relates some function with its derivatives" is technically not correct. For instance, the very first example provided in the page, dy/dx=f(x), is not a differential equation according to this definition since it does not relate y to its derivative. That's why I had changed the definition to "a mathematical equation where one or more derivatives of an unknown function are presents", which I think is more appropriate. Amanfroi (talk) 17:25, 20 June 2019 (UTC)

To editor Amanfroi: The example that you cite was incorrectly stated. I have fixed it. This is true that a formal definition, should be "a mathematical equation that relates some function with its derivatives and its variable(s); the unknown function, the variables or and the derivatives need not to appear all in the equation, although at least one derivative must be present". However such a formal definition would be confusing in the first sentence: The manual of style MOS:MATH#Article introduction recommend: The lead sentence should informally define or describe the subject. So, if a more detailed definition should be given, this should be in the body. I am not sure that it is really useful. D.Lazard (talk) 18:40, 20 June 2019 (UTC)

Not sure how you fixed the first example. It still does not fit the definition given. Since the formal definition you quote says "although at least one derivative must be present", just use that in a simplified definition: an equation where at least one derivative of an unknown function is present. Amanfroi (talk) 20:15, 20 June 2019 (UTC)

Why not separate Linear Differential Equation definition from ODE definition?

@D.Lazard: Just like ODE and PDE are defined with their own section, I think it would be appropriate to define Linear and Non-Linear equations in their own section. Right now the definition of a Linear DE is buried inside the definition of an ODE. But PDE can be linear too. Amanfroi (talk) 17:28, 20 June 2019 (UTC)

When one talks of "linear differential equation" most people think "linear ODE". A witness of this is that in the article Linear differential equation, only the ODE case is considered. Moreover, the theory of linear ODE is well developed and widely taught, while the theory of linear PDE is must less known. It could be said in the section on PDE's that linear PDE's have been considered, but this should require an article to be linked to. Apparently such an article does exists (Linear PDEs redirects to Partial differential equation). Nevertheless, I would not object to add a sentence about linear PDEs in the section on PDEs, if it can be either correctly linked or reliably sourced. D.Lazard (talk) 18:59, 20 June 2019 (UTC)

I respectfully disagree based on how an introductory class on differential equation is often taught. Usually one starts by talking about ODEs and PDEs, Linear and Non-linear, Homogeneous and Non-homogeneous (which could be added). Also, linear PDEs like the diffusion equation, the wave equation, and the Laplace equation, are all taught in an introductory differential equation class.

As a side note, please fix the definition of non-linear equation: "Non-linear differential equations are formed by the products of the unknown function and its derivatives are allowed and its degree is > 1" is not grammatical. It also does not consider non-linear terms like y^(1/2) or sin(y). — Preceding unsigned comment added by Amanfroi (talk • contribs) 20:22, 20 June 2019 (UTC)

 Fixed D.Lazard (talk) 22:18, 20 June 2019 (UTC)

Some software can solve differential equations

Why is it not allowed to mention some programs that are able to solve differential equations: Maple, Mathematica, SageMath, Xcas and ExpressionsinBar among others? Asked by MacApps 25 April 2020 — Preceding unsigned comment added by MacApps (talk • contribs) 16:39, 25 April 2020 (UTC)