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    Systems and Simulation

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    Use the Explicit Modified Euler method to calculate x(h) if h = 0.2, x(0) = 1, and x(t) = (-x^2)(t) - 1.

    The single hat is used to denote the first estimate of a x value and a double hat is used to denote a 2nd estimate .

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    Solution Summary

    The solution to and ODE in the form of x(t) = f(x,t)
    is given by,
    x_(k+1) = x_k + hf[t_k + h/2, x_k + h/2*f(t_k, x_k)]
    where h is the time step and time advances according to tk+1 = tk + h.