M AT 5 14, S pring 2 006
I ntroduction t o O rdinary Differential E quations
F inal E xam F riday, M ay 5
You have 120 minutes to work t he following 7 problems (10 pages). C orrect answers without
complete steps will n ot give full credit. Show A LL your
Yri6;
MAT 514, Fall 2008, Final Exarn
Slrow
ALL your worr. Wt'ite all youl solutiols in clezr.l, logical
Your Name:
steps.
Prcrbern
1. (a) Solve tlie initial value proliletn y/' y' 2U :
lor a so that youl solution in (a) goes to 0 rs 'r
O, y(O)

a, u'(
MAT
514
May 8, 2004
Professor Hsiang
FINAL EXAM
Show your work. No workno credit!
SUID#
I.
Solve the given diflerential equations, i.e., if t,he initial value is given, solve the
problern, otherwise, give the general, solul;ion.
.t
G) :0,  l'a'  a' .
.
iircfw_ *
t.)lr,!,i
MAT 514
_
INTRODUCTION TO ORDINARY DIFFERENTIAI EQUA'TIONS

May 7,2007
[15 points] Given the lirstorder linear system
+ = l:q f l t
dt L 0
FINAL EXAM
1
(a) Compute the eigenvalues;
(b) For eaoh eigenvalue, cotnpute the associated ei
"
NAME:
May 5, 2009
Final Exam
Section
# XX
SSN:XXXX
The exam witl be graded on a partial credit basis. Answers without supporting work
ehown on the paper will receive NO credit.
L.
(20 points) Find a general solution to the equation
2*aa'a212
(20 poi,n
MAT
514
December 16, 2009
Professor Hsiang
FINAL EXAM
Show your work. No workno credit!
SUID#
Name
Solve the given rifferential equations, i.e., if the initial value is given,
problern, otherwise, give the genera,I solution.
du
 t'a' + a'
2t
rxt du \b)
I\cfw_AT 5L4 Final Exam
30
April 2009
This exam has 8 problems on 11 pages (including this cover page).
There is also a table of Laplace transforms.
You have two hours. You must show all your work; correct answers without
complete justification will not r