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math370 - CARLETON UNIVERSITY FINAL EXAMINATION MATH 1005 A...

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CONCORDIA UNIVERSITY Department of Mathematics & Statistics Course Number Section(s) Mathematics MATH 370/MAST 330 01 Examination Date Time Pages Final December 2000 3 hours 2+1 Instructor Course Examiner Pawel G´ora Special Instructions: Calculators permitted. Table of Laplace transforms provided (page 3). Lined paper booklets. MARKS: marks for each problem are shown in front of the problems. Maximum total is 100. MARKS 1) Solve the following equations: 3 (a) xyy = 1 - x 2 , y (1) = 1. 4 (b) ( x 2 + y 2 )d x - xy d y = 0 . 7 (c) x d y d x + 2 y = x 4 . 4 (d) ( x 2 + y 2 + 2 x )d x + 2 xy d y = 0 . 7 (e) y x d x + ( y 3 - ln x )d y = 0 , by finding an integrating factor. 7 2) Find the family orthogonal to the family of curves ( x - c ) 2 + y 2 = c 2 . 7 3) A tank contains 100 gal pure water. Brine containing 2 lb salt per gallon is added to the tank at the rate of 5 gal/min. a) How much salt is present after 20 min if the well stirred mixture runs out at 6 gal/min. b) Find the maximum number of pounds of salt the tank will contain and the number of minutes needed to reach the maximum value.
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