A hand-held calculator will suffice for Problems 1 through 10, where an initial value problem and its exact solution are given. Apply the Runge–Kutta method to approximate this solution on the interval [0,0.5]? with step size h = 0.25. Construct a table showing five-decimal-place values of the approximate solution and actual solution at the points x = 0.25 and 0.5.

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y' = 2y, y(0) = ; y(x) = {e² e2x