HOMEWORK 1 SOLUTIONS: MATH 265
Problem 1: In each case, solve for y(t):
a. y + 2y = 0 with y(0) = 1.
b. y + 2y = 3et with y(0) = 2.
1
c. y 2y = te2t with y( 4 ) = 0.
d. ty 2y = t3 sin t with y() = 0.
3
e. t3 y + 8t2 y = e(t
)
with y(1) = 1.
Solution: Prob
The University of British Columbia
Final Examination - December 2007
Mathematics 265
Section 101
Closed book examination
Last Name:
Time: 2.5 hours
First:
Signature
Student Number
Special Instructions:
- Be sure that this examination has 11 pages. Write y
The University of British Columbia
Final Examination - December 7, 2005
Mathematics 265
All Sections
Closed book examination
Time: 2.5 hours
Special Instructions:
- Be sure that this examination booklet has 4 pages.
- No calculators or notes other than yo
The University of British Columbia
Final Examination - December 2007
Mathematics 265
Section 102
Closed book examination
Last Name:
Time: 2.5 hours
First:
Signature
Student Number
Special Instructions:
- Be sure that this examination has 11 pages. Write y
The University of British Columbia
Final Examination - December 2009
Mathematics 265
Section 101
Closed book examination
Last Name:
Time: 2.5 hours
First:
Signature
Student Number
Special Instructions:
- Be sure that this examination has 13 pages. Write y
Math 265 Final Exam
Monday, December 12, 2011
Duration: 3:30-6pm
Last Name:
First Name:
Student Number:
Do not open this test until instructed to do so!
This exam should have 20 pages, including this cover sheet. The table of Laplace transforms is on Page
The University of British Columbia
Final Examination -December 17, 2010
Mathematics 265
Instructor: Dr. Keshet
Closed book examination
Time: 2.5 hours
LAST Name:
Student #:
FIRST Name:
Signature
Section: 101 / 103 / (Circle one)
Special Instructions: - Be
Some examples of 2nd order linear ODEs with complex and repeated roots 1
1.1
Oscillatory solutions
Pure oscillations, no damping
y + 6y = 0, y (0) = 2, y (0) = 1
Let us consider the equation The characteristic equation is r2 + 6 = 0 which has complex conj
HOMEWORK 1: MATH 265, L Keshet
Due in class on September 22, 2010
Problem 1: In each case, solve for y (t): (a) y + 3y = 2et/2 with y (0) = 1. (b) y 4y = t with y (1) = 0. (c) ty + 2y = sin t with y (/2) = 0. (d) t2 y + 2ty = t3 + 1 with y (1) = 1. Soluti
HOMEWORK 2: MATH 265, L Keshet
(Final version) Due in class on September 29, 2010
NOTE: Most problems on this assignment are straightforward. Problem 4 may take a bit more time and eort.
Problem 1: In each case, solve the following second order ODEs for y
HOMEWORK 4: MATH 265 Due in class on Oct 20 PARTIAL SOLUTIONS
Problem 1: (a) Solve the nonhomogeneous ODE y + 16y = cos(t) with y (0) = 0, y (0) = 0 and express your solution in terms of the frequency of the forcing term > 0. Sketch the solution when = 3
HOMEWORK 5: MATH 265 Due in class on Oct 27
Problem 1: Improper integrals. (a) Consider the integral I = 1 t1 dt. Show that this improper integral converges for p > 1 and nd its p value. Show that it diverges for p = 1. What happens when p < 1? (b) Consid
The University of British Columbia
Final Examination - December 11, 2012
Mathematics 265
Time: 2.5 hours
First
Last Name
Signature
Student Number
Section
Special Instructions:
Books, notes, cellphones and calculators are not allowed.
Use the reverse side
MATH 265 Notes
LINEAR DIFFERENTIAL EQUTUATION
The linear first order differential equation is the first special case of first order
differential equations.
Unlike most of the first order cases, in this case we can actually derive a formula
for the general
Math 265, Fall 2008 Test 2 Solutions
1. Find the Laplace transform of the function shown in the graph.
3
2.5
2
1.5
1
0.5
1
2
3
5
4
-0.5
-1
Solution:
There are two ways to solve this problem: using direct integration, or by writing the
problem as a sum of
MATH 265
Midterm 1
October 20, 2008
D. Coombs
Section 101
Name:
Score
Instructions:
1. Do all 4 given problems.
1
/10
2
/15
3
/10
4
/15
Total
/50
2. Print your name on this page in the space provided.
3. Show all work, partial credit will be given for wri