MAT3700
EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
,UNIVERSITY EXAMINATIONS
October 2025
APM3700
Differential Equations (Engineering)
Duration: 3 hours Marks: 100
Examiners:
First: Mr S Blose
Second: Prof A Adem
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
October 2025
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]
, -3- APM3700
October 2025
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 2025
EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
,UNIVERSITY EXAMINATIONS
October 2025
APM3700
Differential Equations (Engineering)
Duration: 3 hours Marks: 100
Examiners:
First: Mr S Blose
Second: Prof A Adem
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
October 2025
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]
, -3- APM3700
October 2025
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 2025
