Talk:Linear differential equation
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Archives
[edit]Most of the discussions here have recently been archived, but there is no "Archives" section in the talk page header. JonH (talk) 16:44, 4 August 2025 (UTC)
- True ...
- GKNishimoto (talk) 04:19, 21 August 2025 (UTC)
- Fixed (typo). Sorry for that.
- GKNishimoto (talk) 04:29, 21 August 2025 (UTC)
Quadrature
[edit]The first paragraph of "Types of solution" says that some linear differential equations can be "solved by quadrature" and some cannot. The word "quadrature" is linked to Quadrature (mathematics) which seems to be mainly about ruler-and-compass methods, while the disambiguation page says that Numerical integration is often called "numerical quadrature" or simply "quadrature". Quadrature (differential equations) is a redirect to Numerical_integration#Connection_with_differential_equations. This article also says integrals with a link to the Antiderivative article which introduces more terminology.
I don't know what this article is trying to say. If I did, I would edit it to avoid the use of the word "quadrature" and instead mention numerical and analytical solutions, and perhaps I would contrast the integration of a single function with the simulation of the variables in a system of equations. JonH (talk) 14:51, 21 April 2025 (UTC)
- This is fixed. The article gives the right definition of "solving by quadrature". So presently Quadrature (differential equations) redirects here. D.Lazard (talk) 15:35, 21 April 2025 (UTC)
I added links from the section "Types of solution" to two other sections of this article, and they were reverted by @ZergTwo: with the comment "For what reason? Such content is not a quality of a well-written article." This is an answer to that question.
As noted in my comment above, in April I did not understand the word "quadrature". That prompted people to makes changes to Quadrature (mathematics). That article now has a great explanation of how the word has different meanings when applied to differential equations or integrals, and I believe I understand the distinction. I was thinking of restoring the link from the section "Types of solution" to "Quadrature (mathematics)" so that other readers can benefit from the explanation. But then I noticed that the section "Higher order with variable coefficients" does link to "Quadrature (mathematics)". Then I realised that the sections "Higher order with variable coefficients" and "Holonomic functions" expand on the two paragraphs of "Types of solution". Since this is a long article, readers might benefit from extra signposting. There are probably better ways of doing this, but they may need someone to take the time to restructure the article. JonH (talk) 11:40, 22 June 2025 (UTC)
- The term quadrature is clearly causing some confusion. I agree with you that it's not necessary and would be best avoided. The article says in two different places that quadrature means integration - in which case, why not just say integration. Paul Matthews (talk) 22:51, 9 December 2025 (UTC)