Request assistance on how to compute impulse response h(t) for problems, see attachment for symbols and diagrams
1. Compute the impulse response h(t) for dy(t) / dt = 4y(t) = x(t)
2. Compute the impulse response h(t) for dy(t)/ dt - y(t) = dx(t)/dt - 2x(t)
3. A continuous-time system has the input/output relationship, where it is assumed that the system has zero initial energy before the application of the input x(t).
a. Determine the impulse response h(t) of the system.
b. Computer the output response y(t) for 1<t<2 only when the input x(t) is as shown. It is assumed that the system has zero initial energy at time t=0.
This solution uses Laplace transforms and integration to determine the impulse responses for the scenarios as well as the output response at zero initial energy. All steps are shown with brief explanations.