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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
, csc 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.
- Spring '10