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# hw3(6) - t t ∈[0 1-t 2 t ∈(1 2 t> 2 Don’t just use...

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Homework assignment 3 * Due date: December 4, 2006. 1. Perform phase-plane analysis (including a sketch of the direction field) for the following systems: ˙ x = x ˙ y = - y and ˙ x = - x + 2 y ˙ y = - 2 x - y 2. Find the Laplace transforms and their domain for the following functions, defined on [0 , + ): f 1 ( t ) = t n , n is an arbitrary positive integer , f 2 ( t ) = sin( t ) , f 3 ( t ) = cos( t - 1) , f 4 ( t ) = sinh( at ) ,a is an arbitrary real number , f 5 ( t ) =
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Unformatted text preview: t, t ∈ [0 , 1]-t + 2 , t ∈ (1 , 2] , t > 2 Don’t just use the table! 3. Do problems 5.2 # 11 and # 29. 4. Using Laplace transforms, solve the following IVP: ˙ x =-2 x + y, x (0) = 0 ˙ y = x-2 y + sin( t ) , y (0) = 0 5. Do problem 5.8 # 24 (make sure you understand # 23 Frst). * MAP 2302; Instructor: Patrick De Leenheer. 1...
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