# Worksheet: Systems of Ordinary Linear Differential Equations

In this worksheet, we will practice solving systems of linear ordinary differential equations.

Q1:

Find the general solution for the following system of ordinary differential equations:

• A ,
• B ,
• C ,
• D ,

Q2:

Find the general solution for the following system of ordinary differential equations:

• A
• B
• C
• D

Q3:

Suppose that you were tasked with creating a system of ordinary differential equations to model predator-prey dynamics. Let and denote the number of prey (e.g., rabbits) and predators (e.g., foxes), respectively, as a function of time , where the positive numbers , , , and represent parameters that describe how some predator and prey interact with each other. Which of the following systems of first-order nonlinear ordinary differential equations describe such a system?

• A
• B
• C
• D

Q4:

It is possible to convert an -th order differential equation into an -dimensional system of first-order differential equations. For the following 4th-order differential equation, identify the corresponding 4-dimensional system of first-order ordinary differential equations: .

Use the four new variables , , , and to make this determination.

• A , , ,
• B , , ,
• C , , ,
• D , , ,

Q5:

Solve the following system of linear differential equations using matrix methods, giving the matrix

• A
• B
• C
• D

Q6:

Find the general solution for the following system of ordinary differential equations:

• A ,
• B ,
• C ,
• D ,