HW6-2 - y 00 + 3 y + 2 y = 1-u ( t-1) , y (0) = 0 , y (0) =...

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Assignment 6, due Wednesday April 7 MAT 2384C, Winter 2011 Professor Jason Levy, University of Ottawa, Be sure to put your student number on your assignment! 1. Find the Laplace transform of the following functions: ( a ) f ( t ) = 2 e - 2 t sin(3 t ) ( b ) f ( t ) = ( - 3 t + 2 , for 0 t < 5 t, for t > 5 ( c ) f ( t ) = t sin(3 t ) 2. Find the inverse Laplace transform of the following functions: ( a ) F ( s ) = 3 s - 5 s 2 + 4 ( b ) F ( s ) = 1 s 2 + s - 20 3. Use Laplace transforms to solve the initial value problem
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Unformatted text preview: y 00 + 3 y + 2 y = 1-u ( t-1) , y (0) = 0 , y (0) = 1 . Consider the initial value problem y = 3-100 y, y (0) = . (a) Use the forward Euler method, with h = 0 . 5, to estimate y (1). (b) Use the backward Euler method, with h = 0 . 5, to estimate y (1). (c) Which estimate is more accurate? Why? 1...
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