2009_exam2_a - Concordia University Applied Ordinary Differential Equations ENGR 213 Section J Prof Alina Stancu Exam II(A Directions You have 60

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Unformatted text preview: Concordia University March 20, 2009 Applied Ordinary Differential Equations ENGR 213 - Section J Prof. Alina Stancu Exam II (A) Directions: You have 60 minutes to solve the following 4 problems. You may use an admissible calculator. No cell phones are allowed during the exam. (1) (8 points) Determine whether the functions f1 (x) = x, f2 (x) = x2 , f3 (x) = 4x − 3x2 are linearly dependent or linearly independent on the interval (0, ∞). (2) (15 points) Solve the initial value problem y − 2y + 2y = 2x − 2, y (0) = 2, y (0) = 0. (3) (12 points) Solve the differential equation y + y = csc2 x. (4) (5 points) Find a general solution of the differential equation xy + 2y = 0. Useful Formulas: sec x = 1 1 , csc x = , cos x sin x csc u du = ln | csc u − cot u| + C. 1 sec u du = ln | sec u + tan u| + C, ...
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This note was uploaded on 12/07/2011 for the course ENGR 213 taught by Professor Mr.ram during the Spring '10 term at Concordia Canada.

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