Differential Equations

Question 1

What is a differential equation?

Answer 1

One containing a derivative

Question 2

What is the state variable also known as?

Answer 2

The dependent variable

Question 3

A differential equation expresses the rate of change of what?

Answer 3

The state (dependent) variable

Question 4

What is the solution to a differential equation?

Answer 4

An expression for the state variable that makes the differential equation true

Question 5

In dy/dx = 4x^2, what is the state variable?

Answer 5

y

Question 6

For dy/dx = 2y, how do you verify that y = 3e^2x is a solution?

Answer 6

Replace y on both sides with 3e^2x
d/dx (3e^2x) = 2(3e^2x)

Question 7

Is a pure-time differential equation a function of the independent variable or the state variable?

Answer 7

Independent variable

Question 8

Is an autonomous differential equation a function of the independent variable or the state variable?

Answer 8

State variable

Question 9

dP/dt = 1/3P
Autonomous or pure-time?

Answer 9

Autonomous

Question 10

dy/dt = 2y
Autonomous or pure-time?

Answer 10

Autonomous

Question 11

dy/dt = 5t^4 - 12t
Autonomous or pure-time?

Answer 11

Pure-time

Question 12

dy/dt = 2/y^3
Autonomous or pure time?

Answer 12

Autonomous

Question 13

dy/dt = 3 - 1/2t
Autonomous or pure-time?

Answer 13

Pure-time

Question 14

If a solution does not have a value for C, what is it called?

Answer 14

General solution

Question 15

If a solution has a value for C, what is it called?

Answer 15

Particular solution

Question 16

What is the method to estimate a solution to a differential equation from an initial conditions and successive applications of the estimate?

Answer 16

Euler’s Method