20111ee102_1_discussion1

20111ee102_1_discussion1 - y ( ) = T [ x ( )] ,y ( t ) = x...

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WINTER 2011: Discussion: # 1 Posted: January 07 1. Consider the differential equation: dy ( t ) dt + y ( t ) = dx ( t ) dt - 2 x ( t ) , t 0 , y (0) = 0 ,x (0) = 0 . (i) Solve for y ( t ) in terms of x ( t ). (ii) Find y ( t ) given that x ( t ) = ( t - 1) e - t for t > 0. 2. A system has the IPOP description:
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Unformatted text preview: y ( ) = T [ x ( )] ,y ( t ) = x ( t )-2 Z t e t e- x ( ) d, t >- , (i) State all properties of the system (L, NL, TI, TV, C, NC). (ii) Find y ( ) given that x ( t ) = tU ( t ) 1...
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