EXAM
Exam 2
Math 3350–H01, Spring 2012
April 5, 2012
• 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 5 problems. There are 290 points
total.
Good luck!
100 pts.
Problem 1. In each part, find the general solution of the given differential
equation. If initial conditions are given, solve the initial value
problem.
A.
y 00 − 3y 0 + 2y = 0,
y(0) = 1,
y 0 (0) = −2.
B.
y 00 + 6y 0 + 9y = 0.
C.
y 00 + 4y 0 + 13y = 0
D. This is an Euler-Cauchy Equation.
x2 y 00 − 3xy 0 + 4y = 0
40 pts.
Problem 2. Find the general solution.
A. D2 (D − 2)3 (D − 1)y = 0
3
B. (D + 4) (D − (3 + 5i))(D − (3 − 5i)) y = 0
60 pts.
Problem 3. Use the method of Undetermined Coefficients (either version) to find the general solution
A.
y 00 − 3y 0 + 2y = 2x2 + 1.
B.
y 00 − y 0 − 2y = 4xex
C.
y 00 − y 0 − 2y = e−x
40 pts.
Problem 4. Find the general solution of the following differential equation,
using the method of variation of parameters:
y 00 − 2y 0 + y =
1
ex
.
x2
50 pts.
Problem 5. Use the Shifting Rule version of the method of undetermined coefficients to find the general solution of the given
equation. No credit for using any other method (including the book’s
version of undetermined coefficients)!
(D2 + 4)y = cos(2x).
2