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Quiz 3 (4-20-2009) solutions

Quiz 3 4 20 2009 solutions

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Unformatted text preview: AMS 361: Applied Calculus IV by Prof Y. Deng Quiz 3 Monday (04/20/2009) at 8:05-9:25AM for the following DE: Q3-1 (7.5 Points): Find a particular solution where α is a constant and is a given function. You may express the particular in terms of the given in some integral form (5.5 Points). solution Find the again (2.0 Points) for a specific . Solution. We consider two cases: (1) 0. We have . . 1, we have For . . 0. The characteristic equation of the corresponding homogeneous equation is 0, α , α Resulting in solutions , Let (2) Let us force the condition 0 Then Therefore We notice 0 0 So we have 1 1 1 1 Therefore (Grading policy: Please don’t deduct any points for solutions without the above red lines.) So we have 1 1 1 2 1 0 2 2 . 2 Let 1 2 1 2 We found , , , . Therefore We have 2 1 2 For , we get 1 2 2 1 . 2 Q3-2 (7.5 Points): The three linearly independent solutions for a 3rd order linear homogenous equation , , . The Wronskian of the system is defined as are given as 2 1 , 2 , 1 3 3 2 3 1 1 2 2 3 . . Without actually solving the...
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