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MAT 514
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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
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' .
.
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'(