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Unformatted text preview: equations are inconsistent, or if th~ only solutions are trivial, you have either guessed incorrectly or made an error in differentiation or in algebra. The good news: no integration tricks needed in this method. ", :1 Ii ;X,') g(x) , Yp( X) r i I, i, P ( )" b m + b m'l,+ + b m X : OX iX ' . .. m . p '(x)eax , m i \ l"' !, ,sin X P m'( X ) iax cos ,~ xS(Aoxm + +Am) + A ) eax m . ' XS ((Aoxm + . .. + Am) eax cas x +(Boxm + .' . +B~)ea~ sinx) .. . Nates. l:ere f is the smallest ilonnegative i~!eger for which every term in Yp ( x) difers from very term in the complementar functionyc(x). Equivalently, for the three cases, s is, . tne numper, of, times 0 'is a ,.root of, the characteristic ~quation, a is a root of. the characteristic equation, and a t i is a root Qf the characteristic equation, respectively....
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This note was uploaded on 11/02/2009 for the course APMA 2102 taught by Professor Keyes during the Spring '08 term at Columbia.
 Spring '08
 Keyes

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