A storage tank contains a liquid at depth y. The liquid is withdrawn at a rate dependent on the depth. The liquid is supplied to the tank at a sinusoidal rate as a function of time. The differential equation governing the depth of the liquid is given by: dy a(1+ y)15 sin? (1) dt A The parameter values are tank cross-section A = 1200m?, maximum supply Q = 550 m?/day and coefficient a = 160. Assume that the coordinate y was chosen so as y = 1 at t = 0. 1. Use Euler method (described and discussed in Chapter 1 of the textbook), to manually calculate the depth y from t = 0 to 2 days using step size At = 1.0 and 0.5 (measured in days). List your result in a table and plot the elevation of y versus t for the above-listed step sizes, all in one graph. This will be used for verification with the computations below. 2. Write a MATLAB program to implement the Euler method (without using any pre- written MATLAB program/function of the Euler method) to solve the Equation (1) and use it to conduct computations for the depth y from t = 0 to 10 days using step size At = 1.0,0.5, 0.1 and 0.05 (measured in days). Generate printout of the computation results in tables. Plot the elevation of y versus t for the above-listed step sizes, all in one graph for comparison. 3. Please comment on the computation results with the comparison based on the different step sizes and verification with the manual calculation.