Talk:Differential equation
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Flow
[edit]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)
The section on physics
[edit]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
Definition of Differential Equation is not correct
[edit]@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?
[edit]@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
[edit]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)