Talk:Method of undetermined coefficients

I can solve A_n = A A_{n-1} + B A_{n-2}, but how do I go about solving A_n = A A_{n-1} + B A_{n-2} + k?

Many thanks in advance for your help. Pcb21| Pete 13:49, 22 July 2005 (UTC)[reply]

Is that different "A"s you're talking about, "A" and "A_n"? Reorder the equation to get A_n - a A_{n-1} - b A_{n-2} = k. Find solutions for the inhomogeneous and the homogeneous difference equation. Notice that you have a difference eq'n, not a differential eq'n. Probably this is too late, as the stochastics class is already over (right guess?) 134.83.1.225 15:35, 12 December 2005 (UTC)[reply]

Strange Roots yield different answers[edit]

Should it be noted that when differential equations yield repeated or imaginary roots the form of the 'guess' changes? --Bmalicoat 05:26, 1 March 2006 (UTC)[reply]

Yes, it should. Also, more of the theory should be explained. Ruakh 05:56, 1 March 2006 (UTC)[reply]

particular solution[edit]

The examples make a pat description of an extremely simple problem, making it difficult to see how one would provide forms for the particular solutions of more complex equations. The difficult example, on the other hand, is overly complex for some cases.

General theorem[edit]

why no add a complitely general solution that can work as a theorem/formula into which you can simply plug in? —The preceding unsigned comment was added by 128.59.154.21 (talk) 01:50, 29 March 2007 (UTC).[reply]

There is no formula which yields the solution to any inhomogeneous differential equation. The completely general solution is simply what is already described here: find a solution to the complementary equation (i.e., the homogeneous part), and then find a particular solution to the inhomogeneous version. Their sum is the general solution. Rundquist 00:33, 24 June 2007 (UTC)[reply]

Example sections[edit]

Is there any particular reason that this article contains two sections for examples? If they are to be combined, should it be before or after the "Typical forms" section? Also, anybody who knows more about the relationship between this method and the annihilator method, please contribute. Rundquist 00:38, 24 June 2007 (UTC)[reply]

Difference Equations[edit]

It was mentioned that this method can be used to solve difference equations. Is there an example of how this is done? Bvic4 (talk) 17:10, 1 March 2008 (UTC)[reply]

I agree. This seems to be missing from the article. --Blitzer99 (talk) 15:41, 16 March 2021 (UTC)[reply]

"The right hand side of the equation?"[edit]

I think that in the sentence: "a particular solution based on the right hand side of the equation needs to be found", the phrase "the right hand side" should be subtituted with the phrase "the inhomogeneous component" or something of that sort, since it is not mandatory to write the inhomogeneous component on the right hand side, it is only a convention. --Rockyrackoon (talk) 08:59, 11 February 2010 (UTC)[reply]

Citations[edit]

I just added footnotes to the given reference, but it seems wrong. I don't think a book on discrete and combinatorial math will have DEs in it. Does anyone have the book and want to check? 134.173.201.137 (talk) 17:16, 5 March 2010 (UTC)[reply]

Guess[edit]

Is it really just guesswork? --Joshua Issac (talk) 12:41, 8 March 2012 (UTC)[reply]

Classification of constant term[edit]

The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met:^[1]
$c_{i}$ are constants.

g(x) is a constant, a polynomial function, exponential function $e^{\alpha x}$ , sine or cosine functions $\sin {\beta x}$ or $\cos {\beta x}$ , or finite sums and products of these functions ( ${\alpha }$ , ${\beta }$ constants).
— Method of undetermined coefficients#Description of the method

Is there a more compact way of expressing that second hypothesis? For clarity, the current spelled-out version could be given too as an explanation of a more compact term for such a function, but if there is a more compact term for that mouthful I, as a reader, would appreciate knowing it. :)

—2d37 (talk) 00:05, 18 October 2020 (UTC)[reply]

References

^ Zill, Dennis G., Warren S. Wright (2014). Advanced Engineering Mathematics. Jones and Bartlett. p. 125. ISBN 978-1-4496-7977-4.{{cite book}}: CS1 maint: multiple names: authors list (link)

I would like to add that I'm not even sure that the second hypothesis is correct. It is clear that for (finite) "sums of these functions" we can take a sum of the corresponding Ansatz'es (because the differential operator is linear), however the article does not justify that for "products of these functions", taking a product of the corresponding Ansatz'es will guarantee a solution – having done example problems in undergraduate classes I know that this works in many specific cases, but now that I think about it I am unconvinced that it will work in general. The article needs to address this. Joel Brennan (talk) 18:51, 17 January 2022 (UTC)[reply]

[1] Zill, Dennis G., Warren S. Wright (2014). Advanced Engineering Mathematics. Jones and Bartlett. p. 125. ISBN 978-1-4496-7977-4.{{cite book}}: CS1 maint: multiple names: authors list (link)

[1]