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chuang_exam3

chuang_exam3 - x 00 x = sec t(4(15 pts Find the real-valued...

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MATH 107: EXAM 3 No calculators allowed. Your work must be clearly written in order to receive credit. Time: 50 minutes (1) (15 pts) Find the general real-valued solution to the differential equation x 00 + 2 x 0 + x = 4 sin 2 t (2) (5 pts) Suppose that a linear differential equation has characteristic poly- nomial with roots 1 , 2 ± i, 2 ± i and non-homogeneous term 4 te t + e t cos t + t 2 e 2 t sin t Write down the form of your guess for the particular solution if you were using the method of undetermined coefficients. (3) (15 pts) Find the general real-valued solution to the following:
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Unformatted text preview: x 00 + x = sec t (4) (15 pts) Find the real-valued solution for the non-homogeneous initial-value problem: x = ± 3 2-1 1 ² x + ± e 2 t ² x (0) = ± 1 ² (5) (15 pts) Find the general real-valued solution to x = A x where A = 8-6 21 1-1 3-3 2-8 given that the eigenvalues of A are λ =-1 ,-1 , 1 and that the eigenspaces are E-1 = span -3-1 1 E 1 = span -3 1 1...
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