MAT3700 EXAM PACK 2023 22nd May 2023

UNIVERSITY EXAMINATIONS




September-December 2021

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).

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, -2- APM3700
September-December 2021

QUESTION 1
Solve the following differential equations:
1.1  x ln x  dy  ydx  0 . (4)
dy
1.2 cos x  y sin x  1 Hint: Solve as a linear equation  . (8)
dx
1.3  x 2  xy
dy
dx
  xy  y 2 Hint: Let y  vx  . (8)
[20]

QUESTION 2
Find the general solution of the following differential equation using the method of
d 2y dy
undetermined coefficients: 2
2  y  e 2 x . (8)
dx dx
[8]

QUESTION 3
Find the general solution of the following differential equations using D-operator methods:

3.1  
D D 2  1 y  2 sinh x . (7)

3.2 D 2

 2D  1 y  xe x  7 x  2 (9)
[16]

QUESTION 4
Solve for only x by using D-operator methods in the following set of simultaneous
equations:
D  1 y 
2
5Dx  t

 
2Dy  D 2  4 x  2 . (8)
[8]

QUESTION 5
Determine the following:

5.1 
L sin2 t .  (4)

 3  s  1 
5.2 L1  2 . (2)
 s  2s  10 
[6]
[TURN OVER]