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Unformatted text preview: x + 1. Thus a general solution to our equation is also a solution to the homogeneous equation D ( D 2 + 4)( D 25 D + 6)[ u ] = 0 . The characteristic equation r ( r 2 +4)( r 25 r +6) = 0 has the following roots: r = 2 nonrepeated the fundamental solution e 2 x ; r = 3 nonrepeated the fundamental solution e 3 x ; r = 0 nonrepeated the fundamental solution 1; r = 2 i complex conjugate the fund. sol. are cos 2 x and sin 2 x . So, the fundamental solution set is e 2 x , e 3 x , 1, cos 2 x , and sin 2 x . A general solution is u = C 1 e 2 x + C 2 e 3 x + C 3 + C 4 cos 2 x + C 5 sin 2 x = u h + u p . Since the solution to homogeneous equation u 005 u + 6 u = 0 is u h = C 1 e 2 x + C 2 e 3 x , we obtain u p = C 3 + C 4 cos 2 x + C 5 sin 2 x. 2...
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 Spring '08
 TUNCER

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