A hand-held calculator will suffice for Problems through, 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.
y1 = −y, y(0) = 2; y(x) = 2e−x
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