Unformatted text preview: 5 x + c 6 . 25. ±irst, we rewrite the equation in operator Form, that is, ( D 2 − 6 D + 9 ) [ y ] = sin 2 x + x ⇒ ( D − 3) 2 [ y ] = sin 2 x + x . In this problem, the righthand side is a sum oF two Functions. The ²rst Function, sin 2 x , is annihilated by ( D 2 + 4), and the operator D 2 annihilates the term x . Thus A := D 2 ( D 2 + 4) annihilates the Function sin 2 x + x . Applying this operator to the original equation (in operator Form) yields D 2 ( D 2 + 4)( D − 3) 2 [ y ] = D 2 ( D 2 + 4)[sin 2 x + x ] = 0 . (6.9) 367...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Summation, Homogeneity, Original Problem

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