Problem 1 (15 pts)
1. Find the solution of the following equation y’(t) ~ 2ty(t) = 0 with 31(0) : 1.
[O
t = 0 up to and including 153.
. Find the coefﬁcients of the power series solution of y’(t) — 2ty(t) : 0 with y(0) : 1 at
3. Compute the Taylor series
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)
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 (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
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
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.
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
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 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
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 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 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 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 Practice Midterm Exam
October 2nd, 2014
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 (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 (
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 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 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
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 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 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 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 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