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# ELEM DIFF EQUATIONS Math 3

UCI
GPA 3.73

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Adam Crona on Saturday September 12, 2015. The Class Notes belongs to Math 3 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/201867/math-3-university-of-california-irvine in Mathematics (M) at University of California - Irvine.

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Date Created: 09/12/15
Math 3D Additional Judicious Guessing Examples Paul Macklin April 26 2005 The method ofjudicious guessing can be tricky to get the hang of but it is rewarding It can save you a lot of work when compared to variation of parameters even in the longer examplesl Here I hope to help clarify some additional cases of judicious guessing h l7m going to work several of the odd exercises in your text page 164 as well as problem 10 the stumper problem Many thanks to those who contributed ideas on how to solve that problem Winter 2005 Exercises Find a particular solution to each of the following equations 1 y 3ytgill Solution Because the righthand side is a polynomial we expect 1 to be of the form of a polynomial Next notice that the solutions to the homogeneous problem are cost and sint and so neither is nor 1 is a solution to the homogeneous DE So we only expect to need a Sr degree polynomial 1W abtct2dt3 t b 25 3d2 t 2c 6dt and so 1b 20 6dt 311 3a Sbt 3M 3 t31t20t0171 t33d t230 t3b 6d125 3a By equating coef cients of these polynomials we get 1 2 l d c0b7 a7 andso 1 2 1 7777 73 wt 3 3t3tl Solution Because the righthand side is a polynomial times an exponential we expect a particular solution of the form 1W WW 1bt v e vet t vet2vetvet where v is a polynomial of degree at least 2 The solutions to the homogeneous equation are e and e h Because 6 is a solution to the homogeneous equation we need to increase the degree of v by one Because te is not a solution to the homogeneous equation we don7t need to increase the degree of 1 further it is a polynomial of degree 3

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