advertisement

Method of undetermined coefficients Consider the system 0 −2 x = x + et a 1 3 0 where a is an arbitrary constant vector. Which of the following possibilities would you choose as the most economic xp using the method of undetermined coefficients? A. xp = ue t B. xp = ute t + ve t C. xp = u(te t + e t ) D. xp = ute t E. xp = ut 2 e t + vte t + we t Math 215/255 (Section 921) Systems of ODE-s 2015S T1 1/3 Undetermined coefficients (ctd) Consider the system in the previous example. 2 Suppose that a = . Show that xp = ate t . −1 1 Suppose that a = . Show that xp cannot be of the form ute t . 1 1 Now show that for a = 1 xp = 4 −3 t t te + e . −2 0 What is the source of the disparity in the forms for xp in the two examples above? Math 215/255 (Section 921) Systems of ODE-s 2015S T1 2/3 Critical points, linearizations and stability How many critical points does the following system have? x 0 = (2 + x)(y − x), y 0 = (4 − x)(y + x). A. 0 B. 1 C. 2 D. 3 E. 4 Find the linearizations of each of the critical points, and use it to identify the nature of the critical points. Math 215/255 (Section 921) Systems of ODE-s 2015S T1 3/3