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FinalDE07

# FinalDE07 - Final Examination Summer 2007 Differential...

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Final Examination - Summer, 2007. Differential Equations/Linear Algebra MTH 2201 07/06/2007 Time: 2 hours Max.Credit: 60 Answer all the questions. Make your answers precise and write legibly. Calculators are NOT allowed. 1. (a) Solve the following system of linear equations: [5] a + b + c = 0 5 a + 4 b + c + d = 0 10 a + 6 b + + d = 2 6 a = 1 (b) Find the inverse Laplace transform of the following function: [10] Y ( s ) = 2 s + 1 s ( s + 1)( s 2 + 4 s + 6) (c) Use Laplace transform methods to solve the following initial value problem: [5] y + 4 y + 6 y = 1 + e t y (0) = 0 , y (0) = 0 2. (a) Find a fundamental matrix Φ( t ) of the system of ODE [8] x = 3 x - y y = 9 x - 3 y (b) Find the inverse Φ - 1 ( t ) of the fundamental matrix Φ( t ) obtained in part (a). [4] 1

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(c) Find a particular solution ψ ( t ) of [6] x = 3 x - y + 1 y = 9 x - 3 y + 3 using the formula ψ ( t ) = Φ( t ) t 0 Φ - 1 ( s ) f ( s ) ds where f = 1 3 , and Φ( t ) is the fundamental matrix obtained in (a).
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FinalDE07 - Final Examination Summer 2007 Differential...

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