This preview shows pages 1–2. Sign up to view the full content.
Mathematics 2930. Fall 2009 Prelim I I
Thursday, November 19, 2009 7.30 PM  9 PM
Instructions:
•
Write your name, your TA’s name and section number on your exam booklet
•
No calculators, other electronic devices, or notes are allowed in this exam.
•
Give reasons for your answers and show all work
•
There are 5 problems, each worth 20 points. Good luck !
1. (a) (10 points) Find a general solution of:
y

y

2
y
+ 2
y
= 0
(1)
Here,
y
is a function of
x
for all real
x
and
denotes a derivative with respect to
x
.
Make sure that the correct number of arbitrary constants appear in your solution.
Hint
: The fourth degree polynomial equation:
r
4

r
2

2
r
+ 2 = 0
(2)
has two roots
r
1
=
r
2
= 1. First ﬁnd the other two roots
r
3
and
r
4
.
(b) (10 points) Now consider the equation:
y

y

2
y
+ 2
y
=
e
x
(3)
Find a particular solution of (3).
2. (20 points) Determine the unique solution
x
(
t
) of the following problem.
¨
x
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '05
 STAFF

Click to edit the document details