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Di¤erential Equations and Matrix Algebra I (MA 221), Fall Quarter, 1999-2000 WorkSheet 13 Work with one other person. 1) Apply two steps of the Euler method to That is, I want an estimate of x(0:2): dx = 6 ¡ 2x; x(0) = 5 using a step size of h = 0:1: dt 2) Explain the improved Euler method to each other. Then after (and only after) everyone understands the explanations, apply the improved Euler to the DE in (1) to approximate x(0:2): 3) Compare your approximations in (1) and (2) with the analytic solution of the DE. dx = x2 ¡ 3x + 2: Be sure to include the dt equilibrium solutions (ie the trivial solutions) and discuss the stability of each. 4) Give a rough sketch of the direction …eld for