Differential Equations Quizzes, Questions & Answers

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First Order Equations Quizzes

9602 Difference Equation Identify First Order

In this quiz, we are trying to identify first order difference equations, and also spotting elements that stop a problem from being a first order difference equation. The two co...

Questions: 30 | Attempts: 296 | Last updated: Mar 20, 2025

Sample Question
Select the most accurate statement from the choices below.

This is a first order difference equation in common form

This is a first order difference equation that needs rearranging

This is not a first order difference equation at all

9607 Difference Equations Not First Order

This is a quick quiz to help hone your skills in identifying First Order Difference Equations. A first order difference equation in General Form will have the shape : or

Questions: 66 | Attempts: 248 | Last updated: Mar 22, 2025

Sample Question
Which statement best describes the image above :

This is a first order difference equation in general form

This is a first order difference equation, but not in general form

I'm not falling for that one - this isn't a first order DE at all!

9604 Difference Equations Arithmetic

This quiz focuses on assessing understanding of Arithmetic First Order Difference Equations, a fundamental concept in algebra and discrete mathematics. It tests the ability to reco...

Questions: 36 | Attempts: 229 | Last updated: Mar 17, 2025

Sample Question
This is an Arithmetic First Order Difference Equation

True

False

All First Order Equations Quizzes

Separable Equations Quizzes

Separable Equations: Modeling, Implicit Solutions & Uniqueness Considerations

Not every differential equation is separable—can you tell the difference? This quiz helps you sharpen your skills in identifying separable equations and understanding why oth...

Questions: 15 | Attempts: 13 | Last updated: Dec 16, 2025

Sample Question
Which of the following algebraic steps correctly separates the variables for the differential equation dy/dx = y/x?

Integral of y dy = Integral of x dx

Integral of (1/y) dy = Integral of (1/x) dx

Integral of dy = Integral of (y/x) dx

Integral of x dy = Integral of y dx

Applications of Separable Equations: Cooling, Mixing, Logistic & Trigonometric Models

Ready to push your skills further? This quiz explores more advanced separable equations, including those that require substitutions, partial fractions, or careful handling of const...

Questions: 15 | Attempts: 13 | Last updated: Dec 16, 2025

Sample Question
Identify the separable differential equation from the list below.

Dy/dx = x + y

Dy/dx = sin(xy)

Dy/dx = e^(x+y)

Dy/dx = x² + y²

Conceptual Separable Equations & Basic Initial Value Problems

Can you use given information to find a specific solution? In this quiz, you’ll apply initial conditions to separable differential equations to find particular solutions. You...

Questions: 15 | Attempts: 12 | Last updated: Dec 16, 2025

Sample Question
Which of the following is separable?

Dy/dx = x² + 2xy + y²

Dy/dx = eˣ sin(y)

Dy/dx = ln(x+y)

Dy/dx = (x+y)/x

All Separable Equations Quizzes

Exact Equations Quizzes

Exact Differential Equations: Identifying & Solving via ψ(x,y)

Ready to explore one of the most elegant ideas in differential equations? This quiz guides you through recognizing, verifying, and solving exact equations — where expressions...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Which of the following differential equations is exact?

(2x + y)dx + (x + 2y)dy = 0

(x² + y)dx + (xy + 1)dy = 0

(3x² + 2xy)dx + (2x² + 3y)dy = 0

(y² + x)dx + (3xy + 1)dy = 0

All Exact Equations Quizzes

Homogeneous Equations Quizzes

Homogeneous Differential Equations: Basics, Substitution & Models

Are you ready to dive into the structure behind homogeneous differential equations? In this quiz, you’ll explore how equations that depend only on the ratio y/xy/xy/x can be ...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Which of the following differential equations is homogeneous?

Dy/dx = (x² + y)/x

Dy/dx = (2x + 3y)/(x + y)

Dy/dx = y + sin(x)

Dy/dx = xy + 1

Advanced Differential Equations Quiz

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Which of the following first-order differential equations is homogeneous?

Dy/dx = (x + y)/x

Dy/dx = (2x + y + 1)/(x - y)

Dy/dx = (x² + y²)/(xy)

Dy/dx = y/x + sin(x)

Homogeneous Differential Equations: Axis Shifts, Orthogonal Trajectories & Geometry

Step into the world of homogeneous differential equations—where patterns emerge, variables scale together, and clever substitutions unlock powerful solutions. In this quiz, y...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
The differential equation dy/dx = (x – 3y)/(2x + y) is

Linear but not homogeneous

Homogeneous of degree 1

Bernoulli

Exact

All Homogeneous Equations Quizzes

Growth And Decay Quizzes

Half-life, Newton’s Law of Cooling & Conceptual Logistic Growth (Equilibria & Max Growth)

Ready to model how things move toward a target value? In this quiz, you’ll explore equations where the rate depends on the difference between a quantity and a surrounding con...

Questions: 15 | Attempts: 14 | Last updated: Dec 16, 2025

Sample Question
"The rate of change of a population is proportional to the current population" translates to which differential equation?

DP/dt = k

DP/dt = kP

DP/dt = k(P - M)

DP/dt = k/P

Exponential Growth, Decay & Logistic Basics (k, half-life, carrying capacity)

Are you ready to see how real-life change can be modeled with one simple equation? In this quiz, you’ll explore differential equations where the rate of change depends on the...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
A population grows at a rate proportional to its current size. Which differential equation models this situation?

Dy/dt = k(y - 100)

Dy/dt = ky

Dy/dt = k/y

Dy/dt = constant

Exponential Growth/Decay Applications & Intro to Logistic and Cooling Models

Think you can predict the future of a quantity just from its rate? This quiz challenges you to use half-life and doubling time ideas to solve exponential growth and decay problems....

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
A quantity changes at a rate proportional to itself and is currently decreasing. What is the sign of k in dy/dt = ky?

K > 0

K = 0 ‘

K < 0

Cannot determine

All Growth And Decay Quizzes

Top Trending Differential Equations Quizzes

Laplace Transform Quiz: Test!

The 'Laplace Transform Quiz: Test!' evaluates understanding of key concepts in Laplace transforms, essential for students in engineering mathematics. It tests knowledge on properties, inverse transforms, and differential...

Questions: 10 | Attempts: 1356 | Last updated: Mar 21, 2025

Sample Question
$(f*g)(t)=\int ^{t}_{0} {f(v)g(t-v)dv}$

True

False

Math Quiz: Differential Equations Assessment Questions!

Differential equations are mathematical equations relating functions with their derivatives. With these equations the function represents physical quantities and the derivatives their rate of change. These types of equations are...

Questions: 10 | Attempts: 667 | Last updated: Mar 22, 2025

Sample Question
Who invented differential equations?

Isaac Newton

Galileo

Da Vinci

Copernicus

Quiz I D. E.

This quiz focuses on solving and understanding various differential equations, exploring solutions, integrating factors, and orders of differential equations.

Questions: 20 | Attempts: 165 | Last updated: Mar 20, 2025

Sample Question
The solution of differential equation (x-y2) dx +2xy dy=0 is given by

xe(y2/x)=c

Ye(y2/x)=c

Xe(x2/y)=c

Ye(x2/y)=c

Trivia Questions On Differential Equation

Explore key concepts of differential equations through this trivia. Topics include Laplace Transforms, partial differential equations, Fourier series, and Legendre Differential equations. Ideal for enhancing understanding and...

Questions: 28 | Attempts: 535 | Last updated: Mar 19, 2025

Sample Question
1. A Laplace Transform exists when ______

The function is piece-wise continuous

The function is of exponential order

The function is piecewise discrete

The function is of differential order

AP Calculus Test For High School!

Welcome to the “AP Calculus Test!” This quiz is a fantastic opportunity for high school students studying Advanced Placement Calculus worldwide. Calculus, a branch of mathematics, is known for its complexity and...

Questions: 10 | Attempts: 277 | Last updated: Mar 18, 2025

Sample Question
If a = –1/b, b = –1/c, c = –1/d, d = –1/4, what is the value of a?

-4

-1/4

4

0

Recent Differential Equations Quizzes

Modelling & Simulation Quiz

This quiz focuses on modeling and simulation using differential equations, exploring solutions, eigenvalues, and system dynamics.

Questions: 10 | Attempts: 149 | Last updated: Mar 5, 2025

Sample Question
What is the general solution of the following linear plane autonomous system of first order differential equations?

Option 1

Option 2

Option 3

Option 4

Quiz II H. O. D. E.

Quiz II H. O. D. E. assesses understanding of differential equations, focusing on solving various types with given conditions. It evaluates key mathematical skills necessary for advanced studies in engineering and sciences,...

Questions: 15 | Attempts: 218 | Last updated: Mar 21, 2025