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.

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y' = 2y, y(0) = ; y(x) = ²x