Introduction to Differential Equations

Practice Questions

Differential Equations › Introduction to Differential Equations

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1

Suppose a dog is carrying a virus returns to a isolated doggy day care of 40 dogs. Determine the differential equation for the number of dogs who have contracted the virus if the rate at which it spreads is proportional to the number of interactions between the dogs with the virus and the dogs that have not yet come in contact with the virus.

2

State the order of the given differential equation and determine if it is linear or nonlinear.

3

Solve for y

4

State the order of the given differential equation and determine if it is linear or nonlinear.

5

Solve for y

6

Suppose a dog is carrying a virus returns to a isolated doggy day care of 40 dogs. Determine the differential equation for the number of dogs who have contracted the virus if the rate at which it spreads is proportional to the number of interactions between the dogs with the virus and the dogs that have not yet come in contact with the virus.

7

Which of the following three equations enjoy both local existence and uniqueness of solutions for any initial conditions?

8

Which of the following three equations enjoy both local existence and uniqueness of solutions for any initial conditions?

9

Which of the following definitions describe an autonomous differential equation.

10

Which of the following definitions describe an autonomous differential equation.

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