A hand-held calculator will suffice for Problems 1 through 10, where an initial value problem and its exact solution are given. Apply the improved Euler method to approximate this solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing four-decimal-place values of the approximate solution and actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5.

y' = y - x - 1, y(0) = 1; y(x) = 2 + x - e^x