# MAT 3110 Quiz 1 2022 23

```The University of Zambia
Department of Mathematics and Statistics
Mat 3110 Quiz 1
2nd April, 2023
16.00 - 17.00hrs
Instructions:
• Duration is 60 minutes.
First Name: ......................................................................................
Last Name: .......................................................................................
Computer Number: ..........................................................................
Department and School: ........................................................................
Sex: ......................................................................................
Year of Study: .....................................................................
1. Use Laplace transform technique to solve the initial value problem
y ′′ − y ′ = cos (2t) + cos (2t − 12) u (t − 6) ,
(10 marks)
y (0) = −4, y ′ (0) = 0
2. Graph the function f (t) = |2 − t|[u(t − 1) − u(t − 3)] for t ≥ 0, and find its
Laplace transform.
(5 marks)
3. Find
(5 marks)
4t
2
L[e (t + 3t + 5)]
4. Find and sketch the inverse Laplace transform of the following function
F (s) =
e−s
s2
5. Determine the constants α, β, a, and b so that Y (s) =
transform of the solution to the initial value problem
y ′′ + αy ′ + βy = 0,
2s−1
s2 +s+2
is the Laplace
y(0) = a, y ′ (0) = b.
End of Quiz!
1
(5 marks)
(5 marks)
```