Final answer:
To solve the difference equation and analyze the time path, we can use the characteristic equation and find the roots. By finding the roots of the characteristic equation and using the initial conditions, we can determine the specific solution for Yt. This will help us understand how the variable Y changes over time and identify any patterns or trends in the data.
Step-by-step explanation:
To solve the difference equation and analyze the time path, we can use the characteristic equation and find the roots. The characteristic equation for the given difference equation is r^3 + 6r^2 - r - 6 = 0. By finding the roots of this equation, we can determine the general solution for Yt. To solve the equation, we can use the initial conditions to find the particular solution. Based on the initial conditions Yo = 3, Y1 = 0, and Y2 = 5, we can substitute these values into the general solution to obtain the specific solution for Yt.
By solving the given difference equation and analyzing the time path of the solution, we can determine the values of Yt for each time period t. This will help us understand how the variable Y changes over time and identify any patterns or trends in the data. The solution of the difference equation will provide a mathematical representation of the relationship between the different time periods and the corresponding values of Yt.