M251final(sp07) - Name MATH 251 Final Exam Student Number...

MATH 251
Final Exam
May 10, 2007
Name:
Student Number:
Instructor:
Section:
This exam has 13 questions for a total of 150 points. In order to obtain full credit for
partial credit problems, all work must be shown. Credit will not be given for an
answer not supported by work.
THE USE OF CALCULATORS IS NOT PERMITTED IN THIS EXAMINATION.
At the end of the examination, the booklet will be collected.
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
Total:
Do not write in this box.

MATH 251 Spring 2007 Final Exam
1. (5 points) Which of the equations below is a second order, linear, nonhomogeneous, ordinary
differential equation?
a) ( y
′
)
2
- ty = e
t
b) y
′′
+ 2 y
′
=
1
y
c) t
2
y
′′
+ 2 ty
′
+ 4 y = 1
d) y
′′
+ 3 y
′
+ 2 y = 0
e) 2 y
′′′
- 3 y
′′
= t - 1
2. (5 points) Find the solution of the initial value problem
y
′′
+ 4 y = δ ( t ) , y (0) = 0 , y
′
(0) = 1 .
a) y ( t ) = sin 2 t
b) y ( t ) = cos 2 t +
1
2
sin 2 t
c) y ( t ) =
1
2
sin 2 t +
1
2
u
1
( t ) sin 2( t - 1)
d) y ( t ) = cos t + sin t
e) y ( t ) = 2 sin t
Page 2 of 12

MATH 251 Spring 2007 Final Exam
3. (5 points) Consider the initial value problem
t
2
y
′
+ 2 y