Talk:Annihilator method: Difference between revisions

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Difference between Annihilator method and undetermined coefficients

Two methods are not identical. Annihilator method systematically determines which function rather than "guess" in undetermined coefficients, and it helps on several occasions. For example, y+2y'-3=e^x, by using undetermined coefficients, often people will come up with y_p=e^x as first guess but by annihilator method, we can see that the equation reduces to (D+3)(D-1)² which obviously shows that y_p=xe^x. This method should be promoted more than the "undetermined coefficients" because I looked up "undetermined coefficients" on the book before and it took me a long time to solve ODEs but the annihilator method systematically determines the solution and make the whole solving process much quicker. Revenge king (talk) 02:32, 3 December 2008 (UTC)[reply]

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From the examples given in the page about the method of undetermined coefficients, it seems that these two methods are not identical. I have split off the appropriate example from that article and moved it here, since it seemed unrelated to the other two examples given. However, I still don't know exactly how these two methods are related to each other, so if anyone else knows anything about that, please contribute. Also, this article needs to be cleaned up a lot. Rundquist 00:42, 24 June 2007 (UTC)[reply]

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 Two methods are not identical. Annihilator method systematically determines which function rather than "guess" in undetermined coefficients, and it helps on several occasions.
-For example, y''+2y'-3=e<sup>x</sup>, by using undetermined coefficients, often people will come up with y<sub>p</sub>=e<sup>x</sup> as first guess but by annihlator method, we can see that the equation reduces to (D+3)(D-1)<sup>2</sup> which obviously shows that  y<sub>p</sub>=xe<sup>x</sup>
+For example, y''+2y'-3=e<sup>x</sup>, by using undetermined coefficients, often people will come up with y<sub>p</sub>=e<sup>x</sup> as first guess but by annihilator method, we can see that the equation reduces to (D+3)(D-1)<sup>2</sup> which obviously shows that  y<sub>p</sub>=xe<sup>x</sup>. This method should be promoted more than the "undetermined coefficients" because I looked up "undetermined coefficients" on the book before and it took me a long time to solve ODEs but the annihilator method systematically determines the solution and make the whole solving process much quicker.
 [[User:Revenge king|Revenge king]] ([[User talk:Revenge king|talk]]) 02:32, 3 December 2008 (UTC)