Unformatted text preview: ( D 3 + 2 D 2 − 9 D − 18 ) [ y ] = − 18 x 2 − 18 x + 22 . (6.13) Since, D 3 + 2 D 2 − 9 D − 18 = D 2 ( D + 2) − 9( D + 2) = ( D + 2) ( D 2 − 9 ) = ( D + 2)( D − 3)( D + 3) , (6.13) becomes ( D + 2)( D − 3)( D + 3)[ y ] = − 18 x 2 − 18 x + 22 . The auxiliary equation in this problem is ( r + 2)( r − 3)( r + 3) = 0 with roots r = − 2, 3, and − 3. Hence, a general solution to the corresponding homogeneous equation has the form y h ( x ) = c 1 e − 2 x + c 2 e 3 x + c 3 e − 3 x . 369...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, general solution, corresponding auxiliary equation

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