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For a long time i couldn't understand step 2 to step 3 until i realised M'(x)=a(x)M(x). Prehaps this is the key fact. Also the in the example it isn't clear how you got to m(x)=1/x^2 from the previous step.
I learned it as mu not M. Anyone mind if I change it? Broken Segue 02:52, 20 August 2006 (UTC)
- Come on. :) I think M is fine.
Oleg Alexandrov (
talk) 03:11, 20 August 2006 (UTC)
- wow (quick response), I figured this article was dead...I'm probably being overly nitpicky, but most references online seem to use μ or u. Whatever, if it bothers you I don't care that much. Broken Segue 03:29, 20 August 2006 (UTC)
- One of your references uses IF, another one u, and another one mu. I never heard of any "unwritten convention" about which letter is prefered. Oleg Alexandrov ( talk) 03:48, 20 August 2006 (UTC)
Some people may not be used to function notation and may prefer to use dy/dx etc. etc. (ie. me) Would it be a good idea to change the page to include both notations.( Lahoski ( talk) 11:06, 11 March 2008 (UTC))
(Note we do not need to include the integrating constant - we need only a solution, not the general solution)
This comment in the first example misses the point. Even if you add in the integrating constant, it would only cancel out at the end when you have . Hence, changing M(x) in this fashion has no effect on the final solution. Rwilsker ( talk) 17:18, 25 May 2008 (UTC)
In the example, How the hell does -2y/x^3 disappear? —Preceding unsigned comment added by 85.115.156.30 ( talk) 08:42, 20 June 2010 (UTC)
It doesn't "disappear" - just use the quotient rule to see that indeed (y/x^2)'=y'/x^2-2y/x^3. Emil Wiedemann ( talk) 12:03, 8 July 2010 (UTC)
As stated in the introduction: "... multiplying through by an integrating factor allows an inexact differential to be made into an exact differential...".
However, there is not explained if this is always possible and, if yes, why? The page of "inexact differential" gives a well known example of an integrating factor and nothing more.
Rolancito ( talk) 13:46, 8 August 2011 (UTC)
The use of this term in the article is inconsistent with the usual definition of a partial derivative. I can't tell how the expression before multiplying by M(x) is the partial derivative of the same expression that the total derivative is of. I would suggest removing this use of this term unless it can be made clear how exactly it is a partial derivative.-- Jasper Deng (talk) 14:46, 17 August 2014 (UTC)
I was wondering to include guide or mathematical steps in the following part:
"Solving first order linear ordinary differential equations"
Will it be ok? — Preceding unsigned comment added by Prince khan official ( talk • contribs) 05:38, 19 November 2021 (UTC)
No inline citations, only one source and the source does not support the bulk of the information on the page. Most of the page is poorly formatted, both the way the equations are integrated into the article and the overall article layout.
The sole reference was listed under "external links", I have now moved this to the "references" section. The Elysian Vector Fields ( talk) 05:06, 12 March 2023 (UTC)
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| This
level-5 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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For a long time i couldn't understand step 2 to step 3 until i realised M'(x)=a(x)M(x). Prehaps this is the key fact. Also the in the example it isn't clear how you got to m(x)=1/x^2 from the previous step.
I learned it as mu not M. Anyone mind if I change it? Broken Segue 02:52, 20 August 2006 (UTC)
- Come on. :) I think M is fine.
Oleg Alexandrov (
talk) 03:11, 20 August 2006 (UTC)
- wow (quick response), I figured this article was dead...I'm probably being overly nitpicky, but most references online seem to use μ or u. Whatever, if it bothers you I don't care that much. Broken Segue 03:29, 20 August 2006 (UTC)
- One of your references uses IF, another one u, and another one mu. I never heard of any "unwritten convention" about which letter is prefered. Oleg Alexandrov ( talk) 03:48, 20 August 2006 (UTC)
Some people may not be used to function notation and may prefer to use dy/dx etc. etc. (ie. me) Would it be a good idea to change the page to include both notations.( Lahoski ( talk) 11:06, 11 March 2008 (UTC))
(Note we do not need to include the integrating constant - we need only a solution, not the general solution)
This comment in the first example misses the point. Even if you add in the integrating constant, it would only cancel out at the end when you have . Hence, changing M(x) in this fashion has no effect on the final solution. Rwilsker ( talk) 17:18, 25 May 2008 (UTC)
In the example, How the hell does -2y/x^3 disappear? —Preceding unsigned comment added by 85.115.156.30 ( talk) 08:42, 20 June 2010 (UTC)
It doesn't "disappear" - just use the quotient rule to see that indeed (y/x^2)'=y'/x^2-2y/x^3. Emil Wiedemann ( talk) 12:03, 8 July 2010 (UTC)
As stated in the introduction: "... multiplying through by an integrating factor allows an inexact differential to be made into an exact differential...".
However, there is not explained if this is always possible and, if yes, why? The page of "inexact differential" gives a well known example of an integrating factor and nothing more.
Rolancito ( talk) 13:46, 8 August 2011 (UTC)
The use of this term in the article is inconsistent with the usual definition of a partial derivative. I can't tell how the expression before multiplying by M(x) is the partial derivative of the same expression that the total derivative is of. I would suggest removing this use of this term unless it can be made clear how exactly it is a partial derivative.-- Jasper Deng (talk) 14:46, 17 August 2014 (UTC)
I was wondering to include guide or mathematical steps in the following part:
"Solving first order linear ordinary differential equations"
Will it be ok? — Preceding unsigned comment added by Prince khan official ( talk • contribs) 05:38, 19 November 2021 (UTC)
No inline citations, only one source and the source does not support the bulk of the information on the page. Most of the page is poorly formatted, both the way the equations are integrated into the article and the overall article layout.
The sole reference was listed under "external links", I have now moved this to the "references" section. The Elysian Vector Fields ( talk) 05:06, 12 March 2023 (UTC)