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Euler and Modified Euler's method

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I need help using Euler an the improved Euler methods: (look at attachment for better formula display)

1. Consider the initial value problem y' = 2xy, y(1) = 1. Use the Euler's method and improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 1.5. At each step compare the approximate value with the actual value of the analytic solution. Also calculate the bound for the local truncation error using the formula: (look at attachment)

2. Consider the initial value problem ' ( 1) , (0) 2. 2 y = x + y − y = Use the improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution.

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The solution shows how to approximate the result of a first order ordinary differential equation using Euler's method and the modified Euler's method.

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