2. Time-Domain Representations of LTI Systems

If a root r j is repeated p timesin characteristic eqs., thecorresponding solutions arer t r t p1r tContinuous-time case : e , te , ..., t eExample 2.17: RC Circuit: Homogeneous Solutionj j jDiscrete-time case: r , nr , ..., n rn n p1nj j jThe RC circuit depicted in Fig. 2.30 is described by the differentialequationdy t RC y t x tdtDetermine the homogeneous solution of this equation.2.10 SolvingDifferential and Difference Equations1. Homogeneous Eq. :2. Homo. Sol. :3. Characteristic eq. :4. Homogeneous solution:Time-Domain Representations ofLTI Systems63