Dr. Katz DEq Homework Solutions 99

Dr. Katz DEq Homework Solutions 99 - A lgebraic Solutions...

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Algebraic Solutions of Differential Equations 99 n y(x- 2) ! + ( (6.8.2.3) _{2(l_2)(Lie 0 2 [~a+Cb ta+t2+2ec)2 ] (6.8.3) Proposition. Hypotheses as in (6.8.2), if n does not divide a + b + c, then for every integer ~ > 1 which is invertible modulo n, we have dx xdx t d~c\ (6.8.3.0) C (2) I-x] 7- c C (2) 7- + C (2) -7- + d Proof. For every integer m > 2, we readity calculate [.xm- l(x--1)(X-- 2 ) ~ _ d(xm- l (x - 1)(x--2)) d ye } ye dxm-l(x-1)(x-2) dy ye y d(x "+~ -(1 +2) x"+2x "-~) (6.8.3.1) - 3/ (x"-2. x(x-1)(x-2) (a/n b/n c/n ] / ( ) = m+l (a+~b+gc
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.

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