Worksheet: Systems of Ordinary Linear Differential Equations
In this worksheet, we will practice solving systems of linear ordinary differential equations.
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?
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, , ,