MAT3700
Assignment 1
2025
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, question 1 to 4.
Solve the following first-order differential equations, question 1to 4.
QUESTION 1
dy
= 2sin2 xcosx.
(1) cosy dx
(3)
QUESTION 2
dy
(2) (x3 + y 3 ) = 3xy 2 dx
using substitution y = vx.
(7)
QUESTION 3
(3) cotxdy − ydx = (cotx)(3esinx )dx.
(5)
QUESTION 4
dy
+ ytanx = −y 3 secx
(4) dx
(8)
QUESTION 5
Determine if the given differential equation is exact. If it is exact solve it.
(a) (1 + lnx + xy )dx = (1 − lnx)dy.
(6)
(b) (2x2 − y 2 )dx + (x2 − 2xy)dy = 0.
(6)
TOTAL: [35]
[TURN OVER]
Open Rubric