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Unformatted text preview: (7) y 00 + 16 y = tan 4 x. ( Hint: variation of parameters ) (8) xy 00 + y4 x y = x 3 , x > 0. ( Hint: homogeneous part is CauchyEuler ) (9) Determine the form of a particular solution (do not evaluate the coeﬃcients) for the equation y 00 + 6 y + 10 y = xe3 x cos x + cos 2 x. In problems (10–12), determine the Laplace transform of the given function: (10) f ( t ) = 7 e 2 t cos(3 t )2 e 7 t sin(5 t ) . (11) f ( t ) = ( t + 3) 2( e t + 3) 2 . (12) f ( t ) = ± et , ≤ t ≤ 2 , 2 , t > 2 . In problems (13–14), determine the inverse Laplace transform of the given function: (13) F ( s ) = 2 s1 s 24 s + 6 . (14) F ( s ) = 2 s 2 + 3 s1 ( s + 1) 2 ( s + 2) . We will discuss these problems in class on 10/20/10. The key will be posted separately....
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 Spring '08
 TUNCER
 Laplace, Elementary algebra, 50 Minutes

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