ODES are equations that involve some ordinary derivatives, as opposed to partial derivatives of a function. First order ODES are considered in this course. ODEs arise in many contexts of mathematics and natural sciences. Solving an ODE means finding the equation of the dependent variable as a function of the independent variable. The algorithms used in this course to solve ODEs require two conditions: 1. The ODE can be written in the form of dy = f(x, y), and dx 2. The initial value of y(0) = yo is given. In this lab, you will use Euler's Method to solve a given ODE. Using this method, you can find successive values of y given a step size h. This step size defines the difference between two x values. The formula used to find y values is given as: Yi+1 = Yi + f(x, y) h Before applying this formula, the given ODE must be re-written in the form of = f(x,y). dx Step 2. Exercise The motion of a mass is modelled using the following ODE: y + y cost=0 where y is the displacement and t is the time. The initial value of y is yo = 1.241. A. Write R program that finds the values of displacement between 0 t 6 for the following step sizes, h = 0.5, 0.25 and 0.1. Plot the displacement for each case. B. The solution of this ODE is: y = 0.5 esin 2e-sint Plot the displacement for the same range mentioned in part A using this solution and find the absolute and relative errors when h = 0.5 Hint: All angle values must be in radians.