MAT3700
Assignment 1 2024
This assignment covers Study Guide 1, Module 1, Learning Unit 1.
For more explanations and examples refer to the textbook 8th edition chapters 33, 50 and 51
or 9th edition chapters 46,47 and 48.
Submission of this assignment by the due date will give you admission to the examination.
This assignment contributes 10% to your year mark.
Answer questions 1 to 5. Your answers must show your own reasoning.
All answers must be handwritten and scanned. No typed solutions will be accepted.
Solve the following first-order differential equations, questions 1 to 4.
QUESTION 1
dy
cos y sin2 x cos x (3)
dx
QUESTION 2
dy y y
e x using the substitution y vx . (7)
dx x
QUESTION 3
cot xdy ydx cot x 3e sin x dx (5)
QUESTION 4
dy
dx
y xy 3 1 (8)
QUESTION 5
Determine if the given differential equation is exact. If it is exact solve it.
y
5.1 1 ln x x dx 1 ln x dy
5.2 x 2
y 2 dx x 2 2 xy dy 0
(12)
TOTAL: 35
,
Assignment 1 2024
This assignment covers Study Guide 1, Module 1, Learning Unit 1.
For more explanations and examples refer to the textbook 8th edition chapters 33, 50 and 51
or 9th edition chapters 46,47 and 48.
Submission of this assignment by the due date will give you admission to the examination.
This assignment contributes 10% to your year mark.
Answer questions 1 to 5. Your answers must show your own reasoning.
All answers must be handwritten and scanned. No typed solutions will be accepted.
Solve the following first-order differential equations, questions 1 to 4.
QUESTION 1
dy
cos y sin2 x cos x (3)
dx
QUESTION 2
dy y y
e x using the substitution y vx . (7)
dx x
QUESTION 3
cot xdy ydx cot x 3e sin x dx (5)
QUESTION 4
dy
dx
y xy 3 1 (8)
QUESTION 5
Determine if the given differential equation is exact. If it is exact solve it.
y
5.1 1 ln x x dx 1 ln x dy
5.2 x 2
y 2 dx x 2 2 xy dy 0
(12)
TOTAL: 35
,
