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Question: for the following two problems a b determine the exact...

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For the following two problems a) b) Determine the exact solution to the initial value problem Using Excel or MATLAB or the differential equation for the time interval of [0,2] using Eulers and modified Eulers method for dt = 0.4, 0.2 and 0.1 c) Plot the solutions in on eor more graphs against the exact solution d) Compare the relative error or percent error of each methodology and fill in the table accordingly e) Using this result, make an estimate on the reduction of error gained for both methods as we continue to reduce our time step by a factor of 2 Evaluate the functions and both approximations at t = 2. Exact Value dt Eulers Modified Eulers 0.4 0.2 0.1 0.05 Relative Errors 0.40. Eulers Modified Eulers 4 to0.2 to 0.1 to 0.2 Error Reduction Eulers Modified Eulers 0.1 0.05 ApproximationExacr Relative Error: Exact I, y=2y-1, y(0)=1
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