MAT3700 EXAM PACK 2026 - DISTINCTION GUARANTEED

MAT3700
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,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.
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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.
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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 L1  2  (4)
 s  2s  5 
[7]
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, -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
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