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"'ß !, ,sin X P m'( X ) iax cos ß,~ xS(Aoxm + +Am) + A ) eax m . ' XS ((Aoxm + . .. + Am) eax cas ßx +(Boxm + .' . +B~)ea~ sinßx) .. . Nates. l:ere f is the smallest ilonnegative i~!eger for which every term in Yp ( x) difers from èvery 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 iß is a root Qf the characteristic equation, respectively....
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- Spring '08
- Vector Space, ORDINARY DIFFERENTIAL EQUATIONS, homogeneous solution