Consider the initial value problem y\' = 5x - y + 4; y(0) = 8. (you should have
ID: 2974351 • Letter: C
Question
Consider the initial value problem y' = 5x - y + 4; y(0) = 8. (you should have found the exact solution to this in problem 6. You also need the values you found using Euler's method in problem 7. If you haven't done those problems yet, go back and do it first.) The exact solution to the initial value problem at each of the points x = 0-1, 02, 0.3 and 0.4 (rounded to four decimal places) is Fill in the magnitude of the error at each of these points for your estimates with Euler's method using step sizes of h = 0.1 and 0.05 in the following table. Stop and think if decrease in the magnitude of the error as you go from h = 0.1 to h = 0.05 is what you expect. Consider the initial value problem y' = 5x - y + 4; y(0) = 8. Find the exact solution to this problem: y = Consider the initial value problem y' = 5x - y + 4; y(0) = 8. (you should have found the exact solution to this in problem 6, but you don't need that to answer this problem.) Use Euler's method to find approximate values for y at each of the points x = 0.1, 0.2, 0.3, and 0.4. Use a step size of h = 0.1. Fill in the values you obtain in the following table (calculate your values at each step to at least eight figures, and then record your answers rounded to four decimal places): Now find approximate values for y at each of the points x = 0.1, 0.2, 0.3, and 0.4 with the smaller step size of h = 0.05 (again, calculate your values at each step to at least eight figures, and then record your answers rounded to four decimal places):Explanation / Answer
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