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Page 1 of 8Student Name:Student Net ID:MATH 286 SECTION X1 – Introduction to Differential Equations PlusMIDTERM EXAMINATION 3November 20, 2013INSTRUCTOR: M. BRANNANINSTRUCTIONSThis exam 60 minutes long. No personal aids or calculators are permitted.Answer all questions in the space provided. If you require more space to write youranswer, you may continue on the back of the page. There is a blank page at the endof the exam for rough work.EXPLAIN YOUR WORK! Little or no points will be given for a correct answer withno explanation of how you got it. If you use a theorem to answer a question, indicatewhich theorem you are using, and explain why the hypotheses of the theorem are valid.GOOD LUCK!PLEASE NOTE:“Proctors are unable to respond to queries about the interpretation ofexam questions. Do your best to answer exam questions as written.”USEFUL FORMULAS:eB=Xk=01k!Bk=I+B+12!B2+13!B3+. . .x(t) = Φ(t)Φ(a)-1x(a) + Φ(t)ZtaΦ(s)-1f(s)dsabcd-1=1ad-bcd-b-ca
Student Net ID:MATH 286 X1Page 2 of 8Question:123TotalPoints:12142450Score:1. Consider the following first order linear system of differential equations:x01=-3x1+ 2x3x02=x1-x2x03=-2x1-x2.(a) (4 points) Write this system in the vector-matrix formx0=Ax.