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Unformatted text preview: x (0) + 2( sX ( s )x (0)) + 2 X ( s ) = s s 2 + 4 . Thus, X ( s ) = 1 s 2 + 2 s + 2 + s ( s 2 + 2 s + 2)( s 2 + 4) = 1 s 2 + 2 s + 2 + 1 / 10( s2) s 2 + 2 s + 21 / 10( s4) s 2 + 4 . Note that s 2 + 2 s + 2 = ( s + 1) 2 + 1. By checking that table, we have x ( t ) = et sin t + 1 10 et cos t3 10 et sin t1 10 cos 2 t + 2 10 sin 2 t. Exercise 1 Solve x + 3 x = e 2 t , x (0) =1. Exercise 2 Solve x 00 + 4 x = cos t , x (0) = 1, x (0) = 0. Exercise 3 Solve x 00 + 4 x = e2 t cos t , x (0) = 1, x (0) = 0. Solution: 1.6 5 e3 t + 1 5 e 2 t . 2. 2 3 cos 2 t + 1 3 cos t . 3. 58 65 cos 2 t + 9 65 sin 2 t + 7 65 e2 t cos t4 65 e2 t sin t . 2...
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 Spring '09
 T.Qian
 Math, Cos, Boundary value problem

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