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Unformatted text preview: we see that = 1, = 2, and m 1 = 2. Thus, the operator ( D { 1 } ) 2 + 2 2 3 = ( D + 1) 2 + 4 3 annihilates this function. 19. Given function as a sum of two functions. The Frst term, xe 2 x , is of the type (ii) on the page 334 of the text with m = 2 and r = 2; so [ D ( 2)] 2 = ( D + 2) 2 annihilates this function. The second term, xe 5 x sin 3 x , is annihilated by ( D ( 5)) 2 + 3 2 2 = ( D + 5) 2 + 9 2 according to (iv). Therefore, the composition [( D + 2) 2 ( D + 5) 2 + 9] 2 annihilates the function xe 2 x + xe 5 x sin 3 x . 365...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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