Concordia University March 20, 2009

Applied Ordinary Differential EquationsENGR 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.

Useful Formulas: sec x =1

cos x, csc x =

1

sin x,

∫sec u du = ln | sec u + tan u|+ C,

∫csc u du = ln | csc u− cot u|+ C.

1