A function y(t) satisfies the following differential equation: , where δ(t) is the delta function.  Assuming zero initial condition and denoting the unit step function by u(t), y(t) can be of the form

For the system

with u as unit impulse and with zero initial state, the output, y, becomes

A single input single output system with y as output and u as input, is described by

For the above system find an input u(t), with zero initial condition, that produces the same output as with no input and with the initial conditions.