Math 201 Fall 2011 Assignment #2 Solutions
October 1, 2011
Grade problems 1 and 2, 10 marks each, 20 total for this assignment.
1. y = 1/t + u, so,
y =
1
+ u
t2
1
11
1
( + u) + ( + u) 2
2
t
tt
t
1
u
2
2 + +u
t
t
=
=
Thus, the equation for u is u = u/t
Assignment #1
Due: At the START of tutorial on May 18, 2011. No late assignments will be accepted.
1. Find values of m so that the function y = xm is a solution of the dierential equation
x2 y + 2xy 6y = 0 for all x > 0.
2. (a) Verify that the ODE
d2 y
dy
Math 201 Fall 2011 Midterm Exam 2 (B)
October 28, 2011
1. [5 marks] Find the solution of the initial value problem y 2y + 2y = 0, y (0) = 1, y (0) = 0
The auxiliary equation 2 2 + 2 = 0, = 1 i.
So the two linearly independent solutions are y1 = ex cos x
Math 201 Fall 2011 Midterm Exam 2 (A)
October 28, 2011
1. [5 marks] Find the solution of the initial value problem y 4y + 5y = 0, y (0) = 1, y (0) = 5
The auxiliary equation 2 4 + 5 = 0, = 2 i.
So the two linearly independent solutions are y1 = e2x cos
Problems and Solutions
for
Ordinary Diferential Equations
by
WilliHans Steeb
International School for Scientic Computing
at
University of Johannesburg, South Africa
and
by
Yorick Hardy
Department of Mathematical Sciences
at
University of South Africa, So
Math 201
Sections S01 and S02, Spring 02
Midterm Solutions
1.
(a) f is dened on [0, +). Singular solutions (xed points) are found by solving f (x) = 0, which gives
x = 1 and x = 4. Plotting f , we obtain Figure 1.
Figure 1: Exercise 1. Graph of the functi
MATHEMATICS 201 [S01]
Practice Test
Feb. 7, 2002
You may use nonprogrammable, nongraphing calculators.
Note: this test is longer than the actual midterm!
1. Consider the following initial value problems (IVPs)
(i) x = x1/2 ,
x(0) = 0
(ii) x = 1 x1/2 ,
.
.
Question 1.
Solve the initial value
PI
zy + (2z + 1)y = czz
I@) = 1.
Question 2.
m
131 E=tlY f%ree of the following first o&x diffexxmtial equations axe exact. Check the correct
triple in the table.
K
4
Check
(f) y(cos(zy) + 1) dz + 3zy2dy = 0
5.
60
.
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COURSE:
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Question 1.
Find the gene& solution Af ea& of the following diffixexhd ecp&ions. If an initial
condition is given, tid the s
MATHEMATICS 201, Section S01
FINAL EXAM QUESTIONS (Apr. 21, 2001)
Duration: 3 hours
Maximum score: 63
Justify all answers. You may use nonprogrammable, nongraphing calculators.
Marks
1. Find the general solution of the following rst order dierential equ
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rendition is given, find the sdution satisf@g that condition.
(b)
xy2s = y3x3,
.
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MATHEMATICS 201 FOl] k PO21
/h&mber Examinations,
lkfarks
V.Ll
I
Page 1.
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Q.1 Find the general solution of ez& of the following differential equations. If an initial
condition is given, find the solution satisfjhg that c@tion.
2
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1
1.
Solve y + y 6 y = 0 , y (0) = 5 , y (0) = 0
[4 marks]
Using the Laplace transform:
(s Y (s) sy(0) y (0) + (sY (s) y(0) 6(Y (s) = 0
(s Y (s) 5s ) + (sY (s) 5) 6(Y (s) = 0
2
2
s 2Y ( s ) + sY ( s ) 6Y ( s ) = 5s + 5
(s
2
)
+ s + 6 Y ( s ) = 5s + 5
Y (s
fd
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1
Mathematics 201 K01
Instructor: Chedo Barone
June 1, 2006
Midterm #1  Chapters 13
Duration: 50 minutes
Instructions:
1. All questions are fullanswer questions. Write out your solution carefully and
completely on the question paper. Marks will be dedu
Sample Questions for Midterm 3
The following are some questions from the midterm which was given last semester. Since
last semesters exam also included questions from other chapers, this is somewhat shorter
than the midterm you will be writing on Thursday
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Sample Midterm
This is the first midterm test that was given last semester.
You should expect that your first midterm test will be similar in length/types of
questions.
1. Solve the following differential equations and initial value problems.
a) (2 x 2 y
l w
v
x v
w v
fDCYA`bUDrX4TF@9UTiX@FX@Vd'fH4'Dr'aHg3
h h C A q F H A S h S 7 C C C A E 9
2 k
Xpg v pg v
k
hH 9EHFS 9 9 C A CEHi CF V h h C A C S h A H AV 7 q 9 9
'4aFD9aAU'4dXTVD9BA'TH'@rgf7'4eXd@CYAY`'@rXa4YFPDFXTFD9Y4FUTHIah'DrA @Ch
u w

Dvv
v ew y
w
v ev y w
DCcAp dHDsbS4XG@9HXqb@Gb@`g'Q4'DsS'YQi3
p C A rG Q A V p V 7C C C A E 9
m 2 m
id w 4id w
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~
y
ww
1
1.
Solve y 2 y 8 y = 0 , y (0) = 6 , y (0) = 0
[4 marks]
Using the Laplace transform:
(s Y (s) sy(0) y (0) 2(sY (s) y(0) 8(Y (s) = 0
(s Y (s) 6s ) 2(sY (s) 6) 8(Y (s) = 0
2
2
s 2Y ( s ) 2 sY ( s ) 8Y ( s ) = 6s 12
(s
2
)
2 s 8 Y ( s ) = 6s 12
Y (s) =
6
DECEMBER EXAMINATIONS 1991
MATHEMATICS 201, SECTIONS [FOl]&[FO2]
Find the general solution of each of the following differential equations. If
initial condition is given, find the solution satisfflng that condition.
( a ) (3xy+y2)dx + (x2+xy)dy = 0 ,
y(l)
UNIVERSITY OF VICTORIA
COOP EXAMINATIONS, AUGUST 1992
MATHEMATICS 201, SECTIONS [KOl] & [KO2]
puration: u r s
2 h o
Instructor:
WOl] F. Diacu
[KOS] F. Diacu
STUDENTS MUST COUNT THE NUMBER OF PAGES IN THIS EXAMINATION PAPER BEFORE
BEGINNING TO WRITE, AND
MATIIEMATICS 201 ~Ol]&$FO2] Page 1
Final Examinations  December 1992
i.
The three firstorder equations below are each solvable by a special method. Solve any
two of them. Classify the remaining one as to type(vari&les separable, homogeneous
coefficients
MATH 201 MIDTERM 2
Duration: 50 minutes. Please attempt as many problems as you can. If you get
stuck on a problem, try another one and come back to it later. Feel free to use the
backs of pages if you need more space for your work.
1. (a) Are the functio
MATH 201 MIDTERM 1
Duration: 50 minutes. Please attempt as many problems as you can If you get
stuck on a problem, try another one and come back to it later. Feel free to use the
backs of pages if you need more space for your work.
1. Consider the equatio
Math 201  Practice Midterm # 2
Try to do this practice test AFTER you have studied, without looking at your notes or the text
book. The actual midterm will only be about 75% as long as this practice test.
1. Solve the following DEs
a)y 00 4y 0 5y = 0
b)4
Math 201  Practice Midterm
Try to do this practice test AFTER you have studied, without looking at your notes or the text
book. The actual midterm will only be about 75% as long as this practice test.
1. Solve the following IVPs
dy
xy + 2y x 2
a)
=
, y(6