i need help with this using excel

and answering the quotations

Purpose: Find the solution of lst order Ordinary Differential Equations (ODE) using well known methods; namely, Euler's, Runge-Kutta 2nd, 3rd, and 4th Order Methods. Discussion: For the thin, glasswalled mercury thermometer system shown below, assume that the temperature of the bath changes based on certain chemical process occurring between two substances reacting with each other inside the bath. It is found that the ordinary differential equation that describes this process is given as follows: d0 3 + 29(t) : cos(4t) It can be found that the actual solution of the response of the thermometer, 90:), is given by the following equation: 9(t) = 0.1 cos (4t) + 0.2 sin (4:) + 2.9 4-20 Thermometer 1 Bath Requirements: The ODE given above can be solved using many numerical methods, such as Euler's and Runge- Kutta Methods. . Use the following information to find the discrete values of 0(t) at each h step value. . h = 0.8, 0.2, 0.05 0 0 0 = 3 C . O s t s 2 second . Use the following methods: . Euler's Method . Runge-Kutta 2nd order . Runge-Kutta 3rd order . Runge-Kutta 4th order . Calculate the percent relative error of the resultant solution at each time for each h step. . Your output should show a table that shows the following: o exact temperature o estimated temperature o percent relative errorwhat i need help with . The calculations and all pertinent files. . You can use either Excel or C++/C to create this solution. . If using Excel you definitely want to read up on creating macros/functions. . The calculated values. o Submit a screenshot of your calculated values. . Answers to the following questions submitted as either: o a video. o or, as an audio only file, if you are unable to submit a video file. . Questions A: . Which method has the highest accuracy? . Which values for h have the highest accuracy? . What evidence exists to support your choices for the previous questions? . Questions B: . What is a differential equation? . What makes an ordinary differential equation, ordinary? . What is the purpose of the Runge-Kutta methods of numerical analysis