Unformatted text preview: to the associated homogeneous equation, we set s = 2. (Note that this means that r = − 2 will be a root of multiplicity three of the auxiliary equation associated with the operator equation A [ L [ y ]]( x ) = 0, where A is an annihilator of the nonhomogeneous term g ( x ) = e − 2 x and L is the linear operator L := D 3 + 3 D 2 − 4.) Thus, the form of a particular solution to this equation is y p ( x ) = C 1 x 2 e − 2 x . 5. In the solution to Problem 1, we determined that a general solution to the homogeneous di±erential equation associated with this problem is y h ( x ) = c 1 e x + c 2 e 3 x + c 3 e − 2 x , and that a particular solution has the form y p ( x ) = C 1 xe x + C 2 + C 3 x + C 4 x 2 . 362...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Homogeneity, The Roots, Beanie Sigel

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