MATH 2271 - Ordinary Differential Equations
Semester 2, Academic Year 2024/2025
Quiz #2: *Worth 5% of your final mark in this course
Date: Friday 14th March 2025 @ 4:00 pm
Time Limit: 30 minutes
Please answer all questions, showing all your working.
Marks are indicated in square brackets.
1. (a) Solve the homogeneous system of first order ordinary differential equations given by
1 −1
′
x =
x
1 3
x1 (t)
where x =
. Comment on the type and stability of the equilibrium solution
x2 (t)
of this system of equations.
[10]
(b) *You are given that the solution of the homogeneous system of first order ODEs
′
2 −1
3 −2
x =
x
can be expressed as
x = C1
1
1
t
e + C2
1
3
e− t
where C1 and C2 are constants (*Note: No need to verify this).
Use the method of your choice to solve the related non-homogeneous system
of first order ODEs
2 −1
1
′
x =
x+
et
3 −2
−1
and show that your solution can be expressed as:
x = C1
1
1
e t + C2
1
3
e− t +
2
2
End of Question Paper
1

t et + 
− 12
− 32

 e t.
[10]