Chapter 9.2, Problem 2E

Assume that $w_2=\frac{3}{4}\text{in}$ (4). Use the resulting second-order Runge-Kutta method to approximate y(0.5), where y(x) is the solution of the initial-value problem in Problem 1. Compare this approximate value with the approximate value obtained in Problem 11 in Exercises 9.1.

1. 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.