Answer Happy

Use Euler's method with step size 0.5 to compute the approximate y-values y₁ ≈ y(0.5), y2 ≈ y(1), y3 ≈ y(1.5), and y4 ≈ y(2) of the solution of the initial-value problem y = −2+ 3x + 4y, y(0) = −2. Y1 = Y2 = Y3 = Y4= ст
Consider the differential equation with initial condition y(0) = 3. A. Use Euler's method with two steps to estimate y when a = 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!) 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 = dy da = 62, 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?)