Consider the differential equation dy/dx = 2x, with initial condition y(0) = 5.
ID: 2966716 • Letter: C
Question
Consider the differential equation dy/dx = 2x, with initial condition y(0) = 5. Use Euler's method with two steps to estimate y when x = 1: y(1) almost (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!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) What is the solution to this differential equation (with the given initial condition)? y = 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 = 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 =Explanation / Answer
dy/dx = 2x and y(0) = 5
y= x2 + 5
y(1) = 6