Question

Find the response $y(t)$ of an LTIC system described by the equation $\frac{d^2y(t)}{dt^2} + 5\frac{dy(t)}{dt} + 6y(t) = \frac{dx(t)}{dt} + x(t)$ if the input $x(t) = 3e^{-5t}u(t)$ and all the initial conditions are zero; that is the system is in the zero state (relaxed).

          Find the response $y(t)$ of an LTIC system described by the
equation
$\frac{d^2y(t)}{dt^2} + 5\frac{dy(t)}{dt} + 6y(t) = \frac{dx(t)}{dt} + x(t)$
if the input $x(t) = 3e^{-5t}u(t)$ and all the initial conditions are zero;
that is the system is in the zero state (relaxed).

Find the response y(t) of an LTIC system described by the
equation
(d^2y(t))/(dt^2) + 5(dy(t))/(dt) + 6y(t) = (dx(t))/(dt) + x(t)
if the input x(t) = 3e^-5tu(t) and all the initial conditions are zero;
that is the system is in the zero state (relaxed).

Added by Erica S.

Differential Equations

Shepley L. Ross 3rd Edition

Chapter 7

Instant Answer

Solved by Expert Sahil Kumar

Step 1

The input x(t) is given as x(t) = 3e^(-5t)u(t), where u(t) is the unit step function. This means that the input is zero for t < 0 and equal to 3e^(-5t) for t ≥ 0. Show more…

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Find the response y(t) of an LTIC system described by the equation x(t) = 3e^(-5t)u(t) if the input x(t) = 3e^(-5t)u(t) and all the initial conditions are zero; that is, the system is in the zero state (relaxed).