Assignment6 - F ( s ) = tan-1 ( a s ) then f ( t ) = sin (...

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Assignment #6 Due: 12:30 pm on Friday July 29, 2011. No late assignments will be accepted. 1. (a)Solve the following IVP using the Laplace transform. Write your answer as a piecewise-defined function (i.e. without unit-step functions). 2 y 00 + y 0 + 2 y = δ ( t - 5) , y 0 (0) = 0 ,y 0 (0) = 0 . (b) Interpret this d.e. as a modeling for electrical circuit or spring system. (c) Discuss (interpret) the solution of this d.e. for the system you give in (b) for 0 t < 5, shortly after t = 5 and also as t → ∞ . 2. Use the formula for the derivative of a Laplace transform to show that if
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Unformatted text preview: F ( s ) = tan-1 ( a s ) then f ( t ) = sin ( at ) t 3. Solve the following system of equations in terms of real-value functions. (a) X = ±-1-4 1-1 ² X (b) X = -3 2 1-1 4-1 2 X 4. Solve the following differential equations by using a power series about x = 0. (a) (1 + x 2 ) y 00-4 xy + 6 y = 0 (b) (1-x ) y 00 + y = 0 (c) y 00-xy-y = 0 1...
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This note was uploaded on 01/15/2012 for the course MATH 201 taught by Professor Steacy during the Fall '10 term at University of Victoria.

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