# Exam1005W2007wAnswers - CARLETON UNIVERSITY FINAL...

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Unformatted text preview: CARLETON UNIVERSITY FINAL EXAMINATION APRIL 2007 DURATION: 3 HOURS Department Name and Course Number: Mathematics and Statistics, MATH 1005 Course Instructor(s): Dr. A. Alaca, Dr. S. Melkonian, Dr. R. Krechetnikov AUTHORIZED MEMORANDA Non-programmable, non-graphing calculator permitted. 1. The orthogonal trajectories of the family of curves y = kx 3 satisfy the di®erential equation [4] (a) y = 3 y x (b) y = ¡ 3 y x (c) y = x 3 y (d) y = ¡ x 3 y (e) None of these 2. The solution y of the initial-value problem y = x 2 2 y ; y (0) = ¡ 4, satis¯es y (3) = [4] (a) ¡ 7 ( b ) 7 ( c ) 5 ( d ) ¡ 5 (e) None of these 3. A particular solution of the equation y 00 ¡ 4 y + 4 y = 3 e 2 x is given by y p = [4] (a) Ce 2 x (b) Cxe 2 x (c) Cx 2 e 2 x (d) Cx 3 e 2 x (e) None of these 4. The general solution of the equation x 2 y 00 + 5 xy + 13 y = 0 for x > 0 is given by y = [4] (a) e ¡ 2 x [ c 1 cos(3 ln x ) + c 2 sin(3 ln x )] (b) e 2 x [ c 1 cos(3 ln x ) + c 2 sin(3 ln x )] (c) c 1 cos(2 x ) +...
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