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test2 - y 00 6 y 9 y = f t where f t is given by the...

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DEPARTMENT OF MATHEMATICS NORTH CAROLINA STATE UNIVERSITY MATH 341 TEST 2 Spring 2009 On all problems, you must show your work to receive credit. Calculators may be used only to do arithmetic and evaluate the numerical value of expres- sions (for example, e 2 or sin ( . 7)). They may not be used for differentiation, integration, algebra, solving differential equations, graphing, etc. 1. Use the method of undetermined coefficients to find a solution to the given initial value problem. y 00 + 2 y 0 - 3 y = - 8 e t ; y (0) = 0 , y 0 (0) = - 6 2. Find the form of a particular solution to the differential equation
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Unformatted text preview: y 00 + 6 y + 9 y = f ( t ) where f ( t ) is given by the following functions: (a) f ( t ) = 2 t sin(-3 t ) + 7 cos(-3 t ) (b) f ( t ) = te-3 t + 2 e-3 t (c) f ( t ) =-t 2 e t 3. Use the method of variation of parameters to find a general solution to the differential equation. y 00-2 y + y =-3 e t t 4 4. Find the inverse Laplace transform of the following functions. (a) s 2-4 s +7 ( s 2-6 s +9)( s-1) (b) 3 s +6 ( s 2 +2 s +10) TABLE OF LAPLACE TRANSFORMS ON BACK...
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