engr 213 midterm 2b 2009
TRANSCRIPT
![Page 1: Engr 213 midterm 2b 2009](https://reader035.vdocument.in/reader035/viewer/2022071710/55a6c9191a28ab4e1d8b46bc/html5/thumbnails/1.jpg)
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