Can someone answer these question using MATHLAB

This assignment follows the standard form for a project submission. You need to include an introduction, primary discussion, and summary. Include graphs, tables, and images, as necessary, to improve the clarity of your discussion. Your project needs to be both correct and well written. Communication remains a critical component of our modern, technological society. A few notes about format: you MUST use MS Word for your project and use Equation Editor for all mathematical symbols, e.g. z(t) = sin(t) + 1/In(t). If you have any questions about the requirements for this project, ask before you submit. This project introduces approximations to Ordinary Differential Equations using numerical methods. You will program three numerical solvers: Euler's method, Improved Euler's method, and 4^th order Runge-Kutta (RK4). You are required to write your own numerical methods in either MATLAB or MS Excel. You are not allowed to use numerical solvers written by anyone else. Consider the following Initial Value Problem (IVP) where y is the dependent variable and t is the independent variable: y' = sin(t) * (1 - y) with y(0) = y_0 and t greaterthanorequalto 0 Approximate the solution to the IVP using Euler's method with the following conditions: Initial condition y_0 = -1/2: time step h = 1/16, and time interval t elementof [0, 20] Derive the recursive formula for Euler's method applied to this IVP Plot the Euler's method approximation Plot the absolute error between the approximation and the exact solution using a semilog plot Approximate the solution to the IVP using the Improved Euler's method with the following conditions: Initial condition y_0 = -1/2: time step h = 1/16: and time interval t elementof [0, 20] Derive the recursive formula for the Improved Euler's method applied to this IVP Plot the Improved Euler's method approximation Plot the absolute error between the approximation and the exact solution using a semilog plot Approximate the solution to the IVP using the RK4 method with the following conditions: Initial condition y_0 = -1/2: time step h = 1/16, and time interval t elementof [0, 20] Plot the RK4 method approximation Plot the absolute error between the approximation and the exact solution using a semilog plot Consider the following Initial Value Problem (IVP) where y(t) is the dependent function: y' = y - y^2 + 1.14 cos(e^t/2) with y(0) = y_o and t greaterthanorequalto 0 Approximate the solution to the IVP using the Improved Euler's method with the following conditions: Initial condition y_0 = 1: time steps h = 1/8, 1/16, 1/32, 1/64: and time interval t elementof [0, 20]