In general, we are using numerical methods to approximate the solution to dy/dx-f (x, y(x)). Consider the following differential equations dy dx y(O) 2 The exact solution isy-(x-1) +3e* Write a Matlab Program to solve the above differential equation using a. Euler's method 1. b. Second order Runge-Kutta c. Fourth order Runge Kutta d. Predictor corrector. 2. Show a graph of the numerical solutions vs. the exact solution, 3. Show a graph of the errors for different number of points N - 10, 20, 40, etc.... . Show the effect of increasing the number of points on the error. 5. What can you conclude about the order of the method? Comment on the behavior you see and determine which method performed best. 6. A write-up explaining your results and analysis of what is happening with the different methods and why 7. A copy of your codes in the appendix 8. Submit your project in one PDF file named (your name ID number PDF) Contact me if you have any question by email or by phone (4403-4117) Submit you work only through Blackboard In general, we are using numerical methods to approximate the solution to dy/dx-f (x, y(x)). Consider the following differential equations dy dx y(O) 2 The exact solution isy-(x-1) +3e* Write a Matlab Program to solve the above differential equation using a. Euler's method 1. b. Second order Runge-Kutta c. Fourth order Runge Kutta d. Predictor corrector. 2. Show a graph of the numerical solutions vs. the exact solution, 3. Show a graph of the errors for different number of points N - 10, 20, 40, etc.... . Show the effect of increasing the number of points on the error. 5. What can you conclude about the order of the method? Comment on the behavior you see and determine which method performed best. 6. A write-up explaining your results and analysis of what is happening with the different methods and why 7. A copy of your codes in the appendix 8. Submit your project in one PDF file named (your name ID number PDF) Contact me if you have any question by email or by phone (4403-4117) Submit you work only through Blackboard