In class, we saw that if a system specified by a differential equation has non-zero initial conditions, we can include them by using the unilateral Laplace transform. For the differential equation given above in problem 3, now add initial conditions y(0) = 2, y(0) = 3, and x(0) = 4. Write an expression for Y(s) in terms of X(s) and the initial conditions.Consider a continuous-time system described by the following differential equation: 4y(t)-2y(t)=4x(t)+2x(t) (a) Find the system?s transfer function H(s). (b) Draw the poles, zeros, and region of convergence of H(s). assuming that the system is causal. (c) Is the system stable? Why or why not? Recall that y(t) represents the first derivative of y(t), and (t) represents the second derivative (with respect to t).

19 8 - In class, we saw that if a system specified by a differential equation has non-zero initial conditions, we can include them by using the unilateral Laplace transform. For the differential equation given above in problem 3, now add initial conditions y(0) = 2, y(0) = 3, and x(0) = 4. Write an expression for Y(s) in terms of X(s) and the initial conditions.Consider a continuous-time system described by the following differential equation: 4y(t)-2y(t)=4x(t)+2x(t) (a) Find the system?s transfer function H(s). (b) Draw the poles, zeros, and region of convergence of H(s). assuming that the system is causal. (c) Is the system stable? Why or why not? Recall that y(t) represents the first derivative of y(t), and (t) represents the second derivative (with respect to t).

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images - In class, we saw that if a system specified by a differential equation has non-zero initial conditions, we can include them by using the unilateral Laplace transform. For the differential equation given above in problem 3, now add initial conditions y(0) = 2, y(0) = 3, and x(0) = 4. Write an expression for Y(s) in terms of X(s) and the initial conditions.Consider a continuous-time system described by the following differential equation: 4y(t)-2y(t)=4x(t)+2x(t) (a) Find the system?s transfer function H(s). (b) Draw the poles, zeros, and region of convergence of H(s). assuming that the system is causal. (c) Is the system stable? Why or why not? Recall that y(t) represents the first derivative of y(t), and (t) represents the second derivative (with respect to t).

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