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,
( + u) + ( + u) 2
2 + +u
Thus, the equation for u is u = u/t
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
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
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
Ordinary Diferential Equations
International School for Scientic Computing
University of Johannesburg, South Africa
Department of Mathematical Sciences
University of South Africa, So
# OF PAGES: .
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Find the gene& solution Af ea& of the following diffixexhd ecp&ions. If an initial
condition is given, tid the s
Sections S01 and S02, Spring 02
(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]
Feb. 7, 2002
You may use non-programmable, non-graphing calculators.
Note: this test is longer than the actual midterm!
1. Consider the following initial value problems (IVPs)
(i) x = |x|1/2 ,
x(0) = 0
(ii) x = 1 x1/2 ,
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# OF PAGES:
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Find the general solutions of each of the follo&ng differential equations. If ~II Wial
rendition is given, find the sdution [email protected] that condition.
xy2s = y3-x3,
Solve the initial value
zy + (2z + 1)y = czz
I@) = -1.
131 E=tlY f%ree of the following first o&x diffexxmtial equations axe exact. Check the correct
triple in the table.
(f) y(cos(zy) + 1) dz + 3zy2dy = 0
MATHEMATICS 201, Section S01
FINAL EXAM QUESTIONS (Apr. 21, 2001)
Duration: 3 hours
Maximum score: 63
Justify all answers. You may use non-programmable, non-graphing calculators.
1. Find the general solution of the following rst order dierential equ
Solve y 2 y 8 y = 0 , y (0) = 6 , y (0) = 0
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
s 2Y ( s ) 2 sY ( s ) 8Y ( s ) = 6s 12
2 s 8 Y ( s ) = 6s 12
Y (s) =
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Solve y + y 6 y = 0 , y (0) = 5 , y (0) = 0
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
s 2Y ( s ) + sY ( s ) 6Y ( s ) = 5s + 5
+ s + 6 Y ( s ) = 5s + 5
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Mathematics 201 K01
Instructor: Chedo Barone
June 1, 2006
Midterm #1 - Chapters 1-3
Duration: 50 minutes
1. All questions are full-answer questions. Write out your solution carefully and
completely on the question paper. Marks will be dedu
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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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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
1. Solve the following differential equations and initial value problems.
a) (2 x 2 y
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MATHEMATICS 201 FOl] k PO21
Q.1 Find the general solution of ez& of the following differential equations. If an initial
condition is given, find the solution satisfjhg that [email protected]
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 ,
UNIVERSITY OF VICTORIA
CO-OP EXAMINATIONS, AUGUST 1992
MATHEMATICS 201, SECTIONS [KOl] & [KO2]
puration: u r s
2 h o
WOl] F. Diacu
[KOS] F. Diacu
STUDENTS MUST COUNT THE NUMBER OF PAGES IN THIS EXAMINATION PAPER BEFORE
BEGINNING TO WRITE, AND
MAll-l ICMAIICS 201
MID'IERM TEST 2 ('15.\
July 9, 2014
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Name: _. -.m-~.: Student Number: " ~- _ ~ Mm 5
0 Duration: 50 min. Maximum score: 40.
0 Full answers, please. Justify your statements.
0 The test has 4 problems and 4 pages