Differential Equations Quiz: Test Your Knowledge

Question 1

Which of the following is a first-order differential equation?

Accepted Answer

dy/dx + y = x^2

Answer

y'' + y' + y = sin(x)

Answer

d^2y/dx^2 + dy/dx = 0

Answer

d^3y/dx^3 + d^2y/dx^2 + dy/dx = 1

Question 2

The equation dy/dx = xy is an example of what type of differential equation?

Accepted Answer

Separable

Answer

Homogeneous

Answer

Exact

Answer

Linear

Question 3

The general solution of the differential equation dy/dx = 2x is:

Accepted Answer

y = x^2 + C

Answer

y = 2x + C

Answer

y = x^2/2 + C

Answer

y = 2x^2 + C

Question 4

The initial value problem dy/dx = y, y(0) = 1 has the solution:

Accepted Answer

y = e^x

Answer

y = x + 1

Answer

y = e^(-x)

Question 5

Which of the following scenarios can be modeled by a differential equation?

Accepted Answer

The growth of a population over time.

Answer

The area of a rectangle.

Answer

The sum of a sequence of numbers.

Answer

The value of a coin toss.

Question 6

The differential equation describing Newton's Law of Cooling is:

Accepted Answer

dT/dt = k(T - T_a)

Answer

dT/dt = kT

Answer

dT/dt = kT_a

Answer

dT/dt = k(T_a - T)

Question 7

A differential equation is said to be linear if:

Accepted Answer

The dependent variable and its derivatives appear only in a linear combination.

Answer

The dependent variable and its derivatives appear in a product with each other.

Answer

The dependent variable and its derivatives appear only in a quadratic combination.

Question 8

A solution to a differential equation is:

Accepted Answer

A function that satisfies the equation.

Answer

A set of points that satisfy the equation.

Answer

A constant value that satisfies the equation.

Question 9

The general solution of a first-order linear differential equation involves:

Accepted Answer

An arbitrary constant of integration.

Answer

A particular solution and a homogeneous solution.

Answer

A specific value for the dependent variable.

Answer

A set of initial conditions.

Question 10

Which of the following is NOT a step involved in solving a differential equation by separation of variables?

Accepted Answer

Finding a particular solution using an initial condition.

Answer

Separating the variables.

Answer

Integrating both sides of the equation.