1. Solve the following Initial Value Problems: a. y' = 4xe * cosx - y tanx, where y(0) = 1 [3] b. y'=e-Wxy', where y(0) = 1 [3] c. y" = x* + 3y' - 2y, where y(0) = 1, and y'(0) = 3 [3] d. y" + 4y = sin2x, where y(0) = 3, and y'(0) = 3/4 [3] 2. I expect the value of my car to depreciate over the next few years at a constant rate proportional to its current value. a. Model this as a differential equation clearly stating the variables and units of measurements used. Write down the solution to your differential equation. [2] b. When I bought my car brand new it was $23,500 but when I had it valued a few years ago, exactly two and a half years after I bought it, it was f19,200. If it's now six year since I bought the car, what is its value? [4] 3. Short selling is the process of borrowing stocks in a bear market (a declining market), selling them, then buying them back at a reduced cost at some point in the future. For an explanation see Investopia. Suppose the value of a particular stock, ROSN, whose current price is $1000, is expected to satisfy the differential equation, =s'(t) + s(t) =+4 - 58t# + 876 where t is time measured in days, and s (t) is the current value of the ROSN stock. If a trader wants to short sell the ROSN stock when should they buy it back in order to maximise their return? [7]