1. Concordia University March 20, 2009
Applied Ordinary Differential Equations
ENGR 213 - Section J
Prof. Alina Stancu
Exam II (B)
Directions: You have 60 minutes to solve the following 4 problems. You may use an admis-
sible calculator. No cell phones are allowed during the exam.
(1) (8 points) Determine whether the functions
f1 (x) = 1 + x2 , f2 (x) = x, f3 (x) = x2
are linearly dependent or linearly independent on the interval (1, ∞).
(2) (15 points) Solve the initial value problem
y + 2y + 2y = e−2x , y(0) = 0, y (0) = 0.
(3) (12 points) Solve the differential equation
y + y = sec2 x.
(4) (5 points) Find a general solution of the differential equation
xy − 3y = 0.
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Useful Formulas: sec x = , csc x = , sec u du = ln | sec u + tan u| + C,
cos x sin x
csc u du = ln | csc u − cot u| + C.
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