In Problems 1 through 10, an initial value problem and its exact solution y(x) are given. Apply Euler’s method twice to approximate to this solution on the interval [0, 1/2], first with step size h = 0.25, then with step size h = 0.1. Compare the three-decimal-place values of the two approximations at x = 1/2 with the value y(1/2) of the actual solution.

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y' = 2xy2, y(0) = 1; y(x) = 1 1-x²