Consider the differential equation x” + 8x’ + 25x = 10u with zero initial conditions

Question: Consider the differential equation x” + 8x’ + 25x = 10u with zero initial conditions (i.e. x(0)=x'(0)=0) and u(t) is a unit step. Determine the solution y(t) analytically and verify with MATLAB by co-ploting analytic solution and the step response obtained with the step function. (Report should include: Analytic solution, MATLAB Code and outputs, Figure 2. Analytic solution and step response (2 subplots in one image), and conclusion about the system response)

Solution:

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