ODE homework 3 due Tuesday, Jan. 31, 2017
Problems 110 are assigned from Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, 10th Edition. You are
expected to write down every step of the solution and justify your answer.
1. Se
ODE Practice ﬁnal exam
December 16, 2013
Write clearly and Show all work.
This is a closed book test and no calculators are allowed. i
'2
§
3
'2
i
.5
3
{
Problem 1 (15 pts)
Find the solution of the ODE system
92
dt
dy
=w+3y
that satisﬁes the initial con
ODE practice problems for Final
Here is a list of topics that will be covered in midterm 2. For each topic,
some practice problems from the textbook are chosen.
1. Review of power series. Ch 5.1: 8 and 14.
2. Series Solutions near ordinary points. Ch 5.2:
ODE practice problems for midterm 1
Here is a list of topics that will be covered in midterm 1. For each topic,
some practice problems from the textbook are chosen.
1. Linear equation. Ch 2.1: 13 and 14.
2. Autonomous equation and slope eld method. Ch 2.5
ODE practice problems for midterm 1
Here is a list of topics that will be covered in midterm 2. For each topic,
some practice problems from the textbook are chosen.
1. 2nd order Homogeneous equation of constant coecients.
Ch3.1: 4 Ch 3.3: 8 and Ch 3.4: 2
Problem 1 (25 pts)
Find the general solutions of the given differential equations.
1. y’=y+%
2. 4y” —4y’ +y = 0.
JV
1 (4—4;: yum)
a
7}: (H‘éicl‘t
Ckavedew‘sﬂg equatle
4VL— 4H 1:0
Voot: V: i wPemJ V0011. (v:
get/Mai Soiutforx)
\ L
44.41646
g
) l
l
Problem
ODE Practice Midterm Exam
November 14th, 2012
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
20 pts.
20 pts.
20 pts.
20 p
ODE Practice Midterm Exam
October 3rd, 2012
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Total
1
2
3
4
25 pts.
25 pts.
25 pts.
25 pts.
100 pts.
ODE Practice Midterm Exam
November 14 th, 2012
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
20 pts.
20 pts.
20 pts.
20
ODE Practice Midterm Exam
October 3rd, 2012
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Total
1
2
3
4
25 pts.
25 pts.
25 pts.
25 pts.
100 pts.
Problem 1
Find the general solutions of the given dierential equations.
1. y 4y + 4y = 0
2. (2x y)dx + (2y x)dy = 0
Sol:
1. This is a second order equation with constant coecients. The chatecteristic equation
is r2 4r + 4 = 0. This has one repeated root r
Problem 1 (20 pts)
Find the general solutions of the given dierential equations.
1. y 4y = e2t
2. y 4y + 4y = sint
Solution
1. First we solve the homogeneous equation y 4y = 0 . It has characteristic equation
r2 4 = 0 which has roots 2 and 2. Thus the sol
Problem 1 (20 pts)
Find the general solutions of the given dierential equations.
1. y + 4y = 0
2. y 3y + 3y 3y = 0
Solution:
1. The charecteristic equation is r3 + 4r = 0. The roots are 0, 2i and 2i. The general
solutions are y = c1 + c2 sin2t + c3 cos2t
Problem 1
Find the general solutions of the given dierential equations.
1.
dy
dt
+ y = et .
2. (t + 3) dy + y = et .
dt
Sol:
1. This is a linear equation. The integrating factor (t) is (t) = et and the solutions
y(t) are y(t) = (t)1 (t)et dt = et (t + C)
ODE Practice nal exam
December 16, 2013
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
6
7
15 pts.
15 pts
ODE Practice nal exam
December 16, 2013
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
6
7
15 pts.
15 pts
ODE homework 2 due Thursday, Jan. 26, 2017
1. Solve the IVP:
1
y 0 = (1 2x)y 2 , y(0) = .
2
What happens to the solution when x = 2?
2. Determine whether the following ODEs are exact. If it is exact, find
the solution. If it is not, can you find an integr
ODE homework 1 due Tuesday, Jan. 24, 2017
Problems 18 are assigned from Boyce, DiPrima: Elementary Differential
Equations and Boundary Value Problems, 10th Edition. You are expected
to write down every step of the solution and justify your answer.
1. Sec
ODE homework 4 due Thursday, Feb. 2, 2017
1. Suppose a and b are constants and y(t) = c1 eat + c2 et/2 is a solution of
the ODE 6y 00 + by 0 + y = 0 for any c1 , c2 . Find a and b.
2. Find a second order ODE whose general solution is y(t) = c1 et +c2 e2t
ODE homework 5 due Tuesday, Feb. 7th, 2017
Problems 111 are assigned from Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, 10th Edition. You are
expected to write down every step of the solution and justify your answer.
1. P
ODE practice problems for midterm 2
Here is a list of topics that will be covered in midterm 2. For each topic,
some practice problems from the textbook are chosen.
1. Method of undetermined coecient. Ch 3.5: 1, 2 and 3.
2. Variation of parameter . Ch 3.6
ODE Practice Midterm Exam
Nov 18 th, 2015
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
20 pts.
20 pts.
20 pts.
20 pts.
ODE Midterm Exam
October 7th, 2015
Write clearly and Show all work.
This is a closed book test and no calculators are allowed.
Problem 1 5 pts.

Problem 3 4 pts.
Problem 5 5 pts. Problem 1 (5 pts)
Consider the equation I
ﬂy” — 3ty’ + 4y = 0.
ODE Midterm Exam 2
Nov 18th, 2015
Write clearly and Show all work.
This is a closed book test and no calculators are allowed.
Problem 1 5 pts.
Problem 2 6 pts
Problem 3
Problem 4
Problem 5

—
—
Total — Problem 1 (5 pts)
Solve the fo
ODE Practice Midterm Exam
Novr 18 th, 2015
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
20 pts.
20 pts.
20 pts.
20 pts.
ODE Practice Midterm Exam
October7th, 2015
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
20 pts.
20 pts.
20 pts.
20 pts.
ODE Practice Midterm Exam
October 7th, 2015
NAME (please print):
ID:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
20 pts.
20 pts.
20 pts.
20 pts
ODE Practice ﬁnal exam 3—
December 15, 2014
NAME (please print):
ID: ' SCHOOL:
Write clearly and Show all work.
This is a closed book test and no calculators are allowed.
Problem 1 15 ptS.
Problem 2 15 pts.
Problem 3 15 pts.
Problem 4 15 pts.
Proble
ODE Practice ﬁnal exam (L
December 21, 2015
Write clearly and Show all work.
This is a closed book test and no calculators are allowed.
Problem 1 .
Problem 2 15 pts.
Problem 3 15 pts.
Problem 4
Problem 5
Problem 6
Problem 7
m
Total Problem 1 (