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Unformatted text preview: Mathematics 265 Section: Full Name: (circle one) 101 103 Student Number: Midterm Test Oct 6, 2010 Instructions: There are 6 pages in this test (including this cover page). 1. Caution: There may or may not be more than one version of this test paper. 2. Ensure that your full name and student number appears on this page. Circle your section number. 3. No calculators, books, notes, or electronic devices of any kind are permitted. 4. Show all your work. Answers not supported by calculations or reasoning will not receive credit. Messy work will not be graded. 5. Five minutes before the end of the test period you will be given a verbal notice. After that time, you must remain seated until all test papers have been collected. 6. When the test period is over, you will be instructed to put away writing implements. Put away all pens and pencils at this point. Continuing to write past this instruction will be considered dishonest behaviour. 7. Please remain seated and pass your test paper down the row to the nearest indicated aisle. Once all the test papers have been collected, you are free to leave. 8. Exposing your test paper, copying from another students paper, or sharing information about this test constitutes academic dishonesty. Such behaviour may jeopardize your grade on this test, in this course, and your standing at this university. Question Grade Value 1 24 2 16 3 18 4 22 Total 80 I have read and understood the instructions and agree to abide by them. Signed: 1 Problem 1 In each case, solve the ODE for y ( t ): (a) dy dt =- ty 1 / 2 , and y (0) = 1 (b) dy dt = a- 1 t y and y (1) = 0 (where a > 0 is a constant). (c) y + 2 y- 8 y = 0 , and y (0) = 1 ,y (0) = 2 Solution to Problem 1 V2: (a) This equation is nonlinear. We solve it using separation of variables dy y 1 / 2 =- tdt y- 1 / 2 dy =- tdt + C y 1 / 2 1 / 2 =- t 2 2 + C y 1 / 2 =- (1 / 4) t 2 + C . We can use the initial condition now to deduce that....
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