Unformatted text preview: x . Therefore, the composite operator D 2 ( D − 3) = ( D − 3) D 2 annihilates both functions and, hence, there sum. (c) The function x sin 2 x is of the form given in (iv) on page 334 of the text with m = 2, α = 0, and β = 2. Thus, the operator ± ( D − 0) 2 + 2 2 ² 2 = ( D 2 + 4 ) 2 annihilates this function. (d) We again use (iv) on page 334 of the text, this time with m = 3, α = − 2, and β = 3, to conclude that the given function is annihilated by ³ [ D − ( − 2)] 2 + 3 2 ´ 3 = ± ( D + 2) 2 + 9 ² 3 . 386...
View
Full Document
 Spring '10
 Hald,OH
 Math, Differential Equations, Calculus, Linear Algebra, Algebra, Equations, Derivative, e−x cos

Click to edit the document details