Seeking a highly skilled mathematician proficient in Differential Equations to tackle a specific problem using three numerical methods: 1-Euler, 2-Improved Euler, and 3-Runge-Kutta. Please solve each method by hand, dedicating a separate page for each solution.
Ensure that the results obtained from all three methods are extremely close to one another. In case you require assistance during the problem-solving process, refer to the following YouTube video: https://www.youtube.com/watch?v=HWuanyR-5R0&ab_channel=TheMathTutor. This video provides comprehensive lectures on Euler, Improved Euler, and Runge-Kutta Methods.
Once you have the final results from all three methods, kindly plot one of them using Matlab. You do not need to provide the actual code; a single picture of the plot will suffice. Please make sure to maintain clarity and accuracy throughout the solutions and plot.
Looking forward to receiving your excellent work! If there are any questions or clarifications needed, feel free to ask. Thank you for your expertise and dedication.
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