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Homogeneous Equations Quizzes, Questions & Answers

Top Trending Homogeneous Equations Quizzes

Homogeneous DEs: Advanced Forms, Nonlinear Variants & Techniques

Get ready to dive into one of the most elegant corners of differential equations—homogeneous equations, where scaling reveals hidden structure and clever substitutions unlock powerful solutions. In this quiz, you’ll...

Questions: 15 | Attempts: 12 | Last updated: Feb 3, 2026

Sample Question 1
The equation dy/dx = (x + y cos(y/x))/ (x cos(y/x)) is:

Linear

Homogeneous

Exact

Bernoulli

Sample Question 2
Using u = y/x on dy/dx = (3x² + 2 x y + y²)/(x² + 3 x y), what is x du/dx?

(3 + 2u + u² - u(1 + 3u))/(1 + 3u)

(u² - 1)/(1 + 3u)

(2u² + 2u - 3)/(1 + 3u)

U + 2

Sample Question 3
After substitution u = y/x in dy/dx = (4x + 3y)/(x + y), the equation becomes:

X du/dx = u + 3

Du/(u - 4) = dx/x

Du/(3u - 1) = dx/x

X du/dx = (3u + 4)/(u + 1) - u

Recent Homogeneous Equations Quizzes

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, you’ll explore how seemingly complex...

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

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: 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 transformed and solved using powerful...

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