(a) Suppose Y1(t) is a solution of an autonomous system dY/dt = F(Y). Show that Y2(t) = Y1(t +t0) is also a solution for any constant t0. (b) What is the relationship between the solution curves of Y1(t) and Y2(t)?

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d. what is the height of the tide after 93 hours?