Consider the differential equation with initial condition y(0) = 2. A. Use Euler's method with two...

 

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Consider the differential equation with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) ~ (Be sure not to round your calculations at each step!) Now use four steps: y(1) ~ (Be sure not to round your calculations at each step!) dy dx = 6x, B. What is the solution to this differential equation (with the given initial condition)? y = C. What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor = (How close to this is the result you obtained above?) Consider the differential equation with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) ~ (Be sure not to round your calculations at each step!) Now use four steps: y(1) ~ (Be sure not to round your calculations at each step!) dy dx = 6x, B. What is the solution to this differential equation (with the given initial condition)? y = C. What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor = (How close to this is the result you obtained above?)

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For an IVP of the form A For IVP dy da The solution can ... View the full answer