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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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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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