Unformatted text preview: we see that α = − 1, β = 2, and m − 1 = 2. Thus, the operator ± ( D − {− 1 } ) 2 + 2 2 ² 3 = ± ( D + 1) 2 + 4 ² 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 2 = ± ( D + 5) 2 + 9 ² 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, Derivative, ex, ﬁfth derivative operator

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