hw2(4) - • If there are solutions determine them 4 Is e...

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Homework assignment 2 * Due date: October 30. 2006. 1. Determine all real eigenvalues and corresponding eigenfunctions of y ′′ + λy = 0 , y (0) = 0 , y ( π ) + y ( π ) = 0 . 2. Determine the adjoint problem of y ′′ + y - 2 y = 0 , y (0) + y (0) = 0 , y (1) + y (1) = 0 . Is the given problem self-adjoint? 3. Consider the following boundary value problem: y ′′ + y = sin 2 x, y (0) = y (2 π ) , y (0) = y (2 π ) . Using the Fredholm alternative, determine whether or not this problem has solutions.
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Unformatted text preview: • If there are solutions, determine them. 4. Is e − 3 t e − 3 t +3 e 3 t e 3 t e − 3 t e − 3 t-3 e 3 t-e 3 t-e − 3 t-e − 3 t a fundamental matrix solution of ˙ x = 1-2 2-2 1 2 2 2 1 x ? 5. Find a fundamental matrix solution of ˙ x = 1 1 3 1 1 3 1 x * MAP 4305; Instructor: Patrick De Leenheer. 1...
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