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]
27
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]
27
