MAT1512 - Calculus A Assignment 8 2021 memo

MAT1512/101


ASSIGNMENT 08
Fixed Closing Date: 03 September 2021
Total Marks: 25
UNIQUE ASSIGNMENT NUMBER: 703736


1.0 Show whether or not the following differential equations are seperable:


dy x+1
1.1 dx
= y−1
. (3)
dy yex+y
1.2 dx
= x 2 +2
. (3)
dy
1.3 dx
= t(ln(S 2t )) + 8t 2 . (3)

[9]

2.0 Solve the following differential equation by using seperation of variables method


2.1 x dy
dx
= 4y. (3)
dp (1+p2 )cos(t)
2.2 dt
= psin(t)
. (3)

[6]

3.0 Solve the following differential equation subject to the given initial conditions


dy
3.1 dθ
= ysinθ; y(π) = 3. (4)

3.2 x 2 dy
dx
= y − xy ; y(1) = 1. (4)

[8]

4.0 The population of a certain community is known to increase at a rate proportional to the number of
people present at any time. If the population had doubled in 5years, how long will it take to triple? [7]


[Total: 30]




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