Solve the following differential equations:
1.1 x x dy ydx ln 0. (4)
1.2 cos sin Hint: Solve as a linear equation. 1 dy x yx
dx (8)
1.3 2 2 Hint: Let dy x xy y vx dx
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:
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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
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