The dynamic model for a process is given by d2y/dt2+6dy/dt+8y=3u(t) where u(t) is the input function and y(0) and dy/dt(0) are both zero.What are the functions of the time (e.g.,e−t/τ) in the solutionfor each of the following cases?(a)u(t)=be−2t (b) u(t)=ct b and c are constants.Note:You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.