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In this lesson, we will learn how to solve systems of linear ordinary differential equations.

Q1:

Find the general solution for the following system of ordinary differential equations: 𝑦′=𝑦+𝑦,𝑦′=4𝑦+𝑦.

Q2:

Find the general solution for the following system of ordinary differential equations: 𝑦=−𝑦−𝑦,𝑦=2𝑦−4𝑦.

Q3:

Suppose that you were tasked with creating a system of ordinary differential equations to model predator-prey dynamics. Let 𝑥 and 𝑦 denote the number of prey (e.g., rabbits) and predators (e.g., foxes), respectively, as a function of time 𝑡, where the positive numbers 𝛼, 𝛽, 𝛾, and 𝛿 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?

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