MAT3700
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DISCLAIMER & TERMS OF USE
1. Educational Aid: These study notes are designed to serve as educational aids and should not be considered as a
substitute for individual research, critical thinking, or professional guidance. Students are encouraged to
conduct their own extensive research and consult with their instructors or academic advisors for specific
assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information provided in these study notes, the seller cannot guarantee the completeness or correctness of all
the content. It is the responsibility of the buyer to verify the accuracy of the information and use their own
judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their institution's
policies and guidelines regarding plagiarism, citation, and referencing. These study notes should be used as a
tool for learning and inspiration, but any direct reproduction of the content without proper acknowledgment and
citation may constitute academic misconduct.
4. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect damages,
losses, or consequences arising from the use of the notes. This includes, but is not limited to, poor grades,
academic penalties, or any other negative outcomes resulting from the application or misuse of the information
provide
]
,UNIVERSITY EXAMINATIONS
May/June 2022
APM3700
Differential Equations (Engineering)
Duration: 3 hours Marks: 100
Examiners:
First: Ms LE Greyling
Second: Mr S Blose
External: Dr JN Mwambakana
Use of a non-programmable pocket calculator is permissible.
This is a closed book examination and will be IRIS invigilated.
This online paper is the property of UNISA and may not be distributed electronically.
This examination question paper consists of 3 pages including this cover page plus
Formulae sheets (pages 4 to 8) plus
A table of integrals (pages 9 and 10) plus
A table of Laplace transforms (page 11).
Examination rules:
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be password
protected or uploaded as “read only” files).
2. NO emailed scripts will be accepted.
3. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has uploaded.
4. Students are permitted to resubmit their answer scripts within the allocated upload time should
their initial submission be unsatisfactory.
5. Incorrect file format and uncollated answer scripts will not be considered.
6. Incorrect answer scripts and/or submissions made on unofficial examinations platforms will not be
marked and no opportunity will be granted for resubmission.
7. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
8. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
9. Submissions will only be accepted from registered student accounts.
10. Students who have not utilised the IRIS proctoring tool will be subjected to disciplinary processes.
11. Students suspected of dishonest conduct during the examinations will be subjected to disciplinary
processes. UNISA has a zero tolerance for plagiarism and/or any other forms of academic dishonesty.
12. Students are provided one hour to submit their answer scripts after the official examination time.
Submissions made after the official examination time will be rejected by the examination regulations
and will not be marked. E-mail lecturer within the upload hour with screenshots of upload problem
to be assisted with a contingency link. Link closes the same time as the exam platform.
13. Students experiencing network or load shedding challenges are advised to apply together with
supporting evidence for an Aegrotat within 3 days of the examination session.
14. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
or email or refer to Get-Help for the list of
additional contact numbers. Communication received from your myLife account will be considered.
Include screenshots of your problem.
, -2- APM3700
May/June 2022
QUESTION 1
Solve the following first order differential equations:
dy
1.1 x y 2 xy (6)
dx
1.2 sin y 2xy x dx x cos y x dy 0
2 2
[Hint: First show that the equation is exact] (6)
dy ex
1.3 y , given that y (e) 0 (8)
dx x
[20]
QUESTION 2
Find the general solution of the following differential equation using the method of
d 2y dy
undetermined coefficients: 2
5 6y e3x (8)
dx dx
[8]
QUESTION 3
Find the general solution of the following differential equation using D-operator methods:
D 2
6D 9 y x 2e3 x (6)
[6]
QUESTION 4
Solve for x only by using D-operator methods in the following set of simultaneous
equations:
D 1 x 2D 7 y et 2 (10)
2 x D 3 y et 1
[10]
QUESTION 5
Determine the following:
5.1
L e 3t t 2 4 (3)
1
5.2 L1 2 (4)
s 2s 5
[7]
[Page Down]
, -3- APM3700
May/June 2022
QUESTION 6
d 2i di
Determine the current i in the circuit where 2
6 13i 0 if i 0 24 and i 0 4 ,
dt dt
by using Laplace transforms. (8)
[8]
QUESTION 7
Solve the given equation by using Laplace transforms:
y " 4 y 3H (t 4)
The initial values of the equation are y 0 1 and y ' 0 0 . (9)
[9]
QUESTION 8
The conditions in a certain electrical circuit are represented by the following differential
d 2i di
equation: 2 2 2i 85 sin 3t . Determine the general solution for the current, i ,
dt dt
di
in terms of t, given that for t = 0, i = 0 and 20.
dt (10)
[10]
QUESTION 9
1 1 1
If A 4 2 4 , find an eigenvector corresponding to the eigenvalue 2 .
1 1 5
Verify that 2 is an eigenvalue of A. (10)
[10]
QUESTION 10
A periodic function f(x) with period 2 is defined by:
f x 2 x, 0 x 2
Determine the Fourier expansion of the periodic function f(x). (12)
[12]
Full marks = 100
©
UNISA 2022
[Page down]
EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
1. Educational Aid: These study notes are designed to serve as educational aids and should not be considered as a
substitute for individual research, critical thinking, or professional guidance. Students are encouraged to
conduct their own extensive research and consult with their instructors or academic advisors for specific
assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information provided in these study notes, the seller cannot guarantee the completeness or correctness of all
the content. It is the responsibility of the buyer to verify the accuracy of the information and use their own
judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their institution's
policies and guidelines regarding plagiarism, citation, and referencing. These study notes should be used as a
tool for learning and inspiration, but any direct reproduction of the content without proper acknowledgment and
citation may constitute academic misconduct.
4. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect damages,
losses, or consequences arising from the use of the notes. This includes, but is not limited to, poor grades,
academic penalties, or any other negative outcomes resulting from the application or misuse of the information
provide
]
,UNIVERSITY EXAMINATIONS
May/June 2022
APM3700
Differential Equations (Engineering)
Duration: 3 hours Marks: 100
Examiners:
First: Ms LE Greyling
Second: Mr S Blose
External: Dr JN Mwambakana
Use of a non-programmable pocket calculator is permissible.
This is a closed book examination and will be IRIS invigilated.
This online paper is the property of UNISA and may not be distributed electronically.
This examination question paper consists of 3 pages including this cover page plus
Formulae sheets (pages 4 to 8) plus
A table of integrals (pages 9 and 10) plus
A table of Laplace transforms (page 11).
Examination rules:
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be password
protected or uploaded as “read only” files).
2. NO emailed scripts will be accepted.
3. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has uploaded.
4. Students are permitted to resubmit their answer scripts within the allocated upload time should
their initial submission be unsatisfactory.
5. Incorrect file format and uncollated answer scripts will not be considered.
6. Incorrect answer scripts and/or submissions made on unofficial examinations platforms will not be
marked and no opportunity will be granted for resubmission.
7. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
8. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
9. Submissions will only be accepted from registered student accounts.
10. Students who have not utilised the IRIS proctoring tool will be subjected to disciplinary processes.
11. Students suspected of dishonest conduct during the examinations will be subjected to disciplinary
processes. UNISA has a zero tolerance for plagiarism and/or any other forms of academic dishonesty.
12. Students are provided one hour to submit their answer scripts after the official examination time.
Submissions made after the official examination time will be rejected by the examination regulations
and will not be marked. E-mail lecturer within the upload hour with screenshots of upload problem
to be assisted with a contingency link. Link closes the same time as the exam platform.
13. Students experiencing network or load shedding challenges are advised to apply together with
supporting evidence for an Aegrotat within 3 days of the examination session.
14. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
or email or refer to Get-Help for the list of
additional contact numbers. Communication received from your myLife account will be considered.
Include screenshots of your problem.
, -2- APM3700
May/June 2022
QUESTION 1
Solve the following first order differential equations:
dy
1.1 x y 2 xy (6)
dx
1.2 sin y 2xy x dx x cos y x dy 0
2 2
[Hint: First show that the equation is exact] (6)
dy ex
1.3 y , given that y (e) 0 (8)
dx x
[20]
QUESTION 2
Find the general solution of the following differential equation using the method of
d 2y dy
undetermined coefficients: 2
5 6y e3x (8)
dx dx
[8]
QUESTION 3
Find the general solution of the following differential equation using D-operator methods:
D 2
6D 9 y x 2e3 x (6)
[6]
QUESTION 4
Solve for x only by using D-operator methods in the following set of simultaneous
equations:
D 1 x 2D 7 y et 2 (10)
2 x D 3 y et 1
[10]
QUESTION 5
Determine the following:
5.1
L e 3t t 2 4 (3)
1
5.2 L1 2 (4)
s 2s 5
[7]
[Page Down]
, -3- APM3700
May/June 2022
QUESTION 6
d 2i di
Determine the current i in the circuit where 2
6 13i 0 if i 0 24 and i 0 4 ,
dt dt
by using Laplace transforms. (8)
[8]
QUESTION 7
Solve the given equation by using Laplace transforms:
y " 4 y 3H (t 4)
The initial values of the equation are y 0 1 and y ' 0 0 . (9)
[9]
QUESTION 8
The conditions in a certain electrical circuit are represented by the following differential
d 2i di
equation: 2 2 2i 85 sin 3t . Determine the general solution for the current, i ,
dt dt
di
in terms of t, given that for t = 0, i = 0 and 20.
dt (10)
[10]
QUESTION 9
1 1 1
If A 4 2 4 , find an eigenvector corresponding to the eigenvalue 2 .
1 1 5
Verify that 2 is an eigenvalue of A. (10)
[10]
QUESTION 10
A periodic function f(x) with period 2 is defined by:
f x 2 x, 0 x 2
Determine the Fourier expansion of the periodic function f(x). (12)
[12]
Full marks = 100
©
UNISA 2022
[Page down]
