MATH 2070U/2072UTest 7Instructor: D.A. AruliahWeek 13, 2008Name (last name, first name):Student Number:Teaching Assistant:Instructions•Before starting,read over the entire test carefully.•Please verify that the test has 5 pages.•You may use a calculator and a pen or pencil.•Test written in pencil are not elegible for regrading.•Laptops, cellphones, and pagers are not permitted.•Have your student card on your desk.•There are 4 questions on this test and a total of 20 marks.•There are 45 minutes for the test.•Questions do not carry equal weight so use your time wisely.•Show as much work as needed to fully answer the questions.•Write your answers as neatly as possible in the test itself.•You are expected to comply with the UOIT rules for academic conduct.Q:1234TotalMks:466420

MATH 2070U/2072UTest 7Page 2 of 51. [4 marks] Reduce the fourth-order initial-value problemx(0) =-1,x000-x0ln(x00)-t2= 0,x0(0) =12,x00(0) =13to an equivalent first-order system of ODEs1.

MATH 2070U/2072UTest 7Page 3 of 52. [6 marks] Consider the initial-value problem