90 pts.
Problem 1. In each part, find the general solution or solve the initial value
problem.
A.
y 00 + y 0 − 6y = 0,
y(0) = 7,
y 0 (0) = −11.
B.
y 00 + 6y 0 + 9y = 0.
C.
y 00 + 6y 0 + 34y = 0.
D.
x2 y 00 + 5xy 0 + 4y = 0.
40 pts.
Problem 2. Find the general solution.
A. D2 (D − 2)3 (D − 1)y = 0
B. (D + 4)(D2 + 4D + 13)3 y = 0
60 pts.
Problem 3. Use the method of Undetermined Coefficients (either version) to find the general solution
A.
y 00 − y 0 − 2y = x2 + 2
B.
y 00 − y 0 − 2y = xex
C.
y 00 − 2y 0 + y = ex .
1
40 pts.
Problem 4. Find the general solution by the method of variation of parameters.
A.
y 00 − 4y 0 + 4y =
e2x
x2
B.
x2 y 00 + 2xy 0 − 6y = x3
You may assume the solution of the homogenous equation is y = C1 x2 +
C2 /x3 .
2
EXAM
Exam 2
Math 3350, Summer II, 2009
July 27, 2009
• Write all of your answers on separate sheets of paper.
You can keep the exam questions when you leave.
You may leave when finished.
• You must show enough work to justify your answers.
Unless otherwise instructed,
give exact answers, not
√
approximations (e.g., 2, not 1.414).
• This exam has 4 problems. There are 230 points
total.
Good luck!