APM1514
ASSIGNMENT 3 2024
, APM1514/101/0/2024
Tutorial Letter 101/0/2024
Mathematical Modelling
APM1514
Year module
Department of Mathematical Sciences
Problems: Assignment 3
BAR CODE
university
Learn without limits.
Open Rubric of south africa
, ASSIGNMENT 03
Due date: Friday, 24 May 2024
Total Marks: 100
ONLY FOR YEAR MODULE
This assignment covers study unit 4 in the study guide.
Question 1: 12 Marks
Which of the following differential equations are separable or inseparable? Justify your answer algebraically
(hint: demonstrate manipulation up until the form (... )dy = (... )dt or (... )dy = (... )dx, if separable).
(1.1)
dy y
et = − ln(t ) + 8 .
dt t
(1.2)
x 5 dy sin(x + y ) + sin(x− y )
= .
y dx 2
(1.3)
dy cos(x − y ) − cos(x + y )
(y 7 − 1) = .
dx 2
Question 2: 40 Marks
Find the general solutions to the following differential equations:
(2.1)
dx
+ 4x − 1 = 0.
dt
(2.2)
dy
x = 2(y − 4).
dx
(2.3)
dy ty + 3t − 3 − y
= .
dt 4y + ty − 8 − 2t
28
ASSIGNMENT 3 2024
, APM1514/101/0/2024
Tutorial Letter 101/0/2024
Mathematical Modelling
APM1514
Year module
Department of Mathematical Sciences
Problems: Assignment 3
BAR CODE
university
Learn without limits.
Open Rubric of south africa
, ASSIGNMENT 03
Due date: Friday, 24 May 2024
Total Marks: 100
ONLY FOR YEAR MODULE
This assignment covers study unit 4 in the study guide.
Question 1: 12 Marks
Which of the following differential equations are separable or inseparable? Justify your answer algebraically
(hint: demonstrate manipulation up until the form (... )dy = (... )dt or (... )dy = (... )dx, if separable).
(1.1)
dy y
et = − ln(t ) + 8 .
dt t
(1.2)
x 5 dy sin(x + y ) + sin(x− y )
= .
y dx 2
(1.3)
dy cos(x − y ) − cos(x + y )
(y 7 − 1) = .
dx 2
Question 2: 40 Marks
Find the general solutions to the following differential equations:
(2.1)
dx
+ 4x − 1 = 0.
dt
(2.2)
dy
x = 2(y − 4).
dx
(2.3)
dy ty + 3t − 3 − y
= .
dt 4y + ty − 8 − 2t
28
