The graph below shows the response of a system with n poles (denoted by an x) to a non-zero initial conditions. This response is characteristic of the transient response of the system. You can add poles to the system by changing the number of poles. You can change pole locations by dragging them on the complex plane. Note that the DEQ is given in transfer function form. You should be able to convert between transfer function and DEQ form .
where x(n) = dnx/dtn