Use the RK4 method with h = 0.1 to approximate y(0.5), where y(x) is the solution of the initial-value problem y' = (x + y - 1)², y(0) = 2. Compare this approximate value with the actual value obtained in Problem 11 in Exercises 9.1.

Problem 11

Consider the initial-value problem y' = (x + y - 1)², y(0) = 2. Use the improved Euler’s method with h = 0.1 and 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.