Question

Which one of the following is a homogeneous differential equation?

• A. \( \frac{dy}{dx} = x^3 + (\sin x)y \)
• B. \( \frac{dy}{dx} = (x^3 + y^3)e^{\frac{x}{\sqrt{y}}} \)
• C. \( \frac{dy}{dx} = (x^2 + y^2) = 2xy \, dy \)
• D. \( \frac{dy}{dx} = x + e^y \)

Hint:

To identify homogeneous differential equations, check if the degree of the terms on both sides of the equation is the same.

Answer 1

The Correct Option is C

A homogeneous differential equation is one in which the degree of each term in the equation is the same. The correct choice for a homogeneous differential equation is option (3) as it satisfies this criterion. Thus, the correct answer is option (3).