Math 2310H , Fall 2002, Third Exam
Directions : This exam is worth 100 points. You will have seventy-fiv e min utes
to complete this exam. You may not use calculators, but they will not be necessary .
Please show all of your work. If you need scratc h pap er, please use the extra page
at the end of this exam. You do not have to simplify your answ ers once you'v e
done what the problem has asked you to do (e.g. after completing an integration,
you don't have to do go any further). This exam should have 8 pages. Go od luck!
Name:
Problem Possible Score
1 20
2 15
3 15
4 15
5 15
6 20
Total 100
1
2
1. (20 points) The two fundamental solutions to y00 +y = 0 are y1 = C1 sin(x);
and y2 = C2 cos(x) (there are many equivalent solutions, but these are the most
convenient to use for this problem, and will make it work as nicely as possible). Use
this fact and the method of variation of parameters to find a particular solution to
y00 +y = cos(x)sin(x):
3
2. (15 ponts) Find a solution to the system
...
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