Which of the following is a homogeneous differential equation?(A) `(4x + 6y + 5) dy (3y + 2x + 4) dx = 0`(B) `(x y)dx-(x^3+y^3)dy=0`(C) `(x^3+2y^2)dx+2x ydy=0`(D) `y^2dx+(x^2-x y-y^2)dy=0`

Explanation

To determine which of the given options is a homogeneous differential equation, we need to recall the definition of a homogeneous function. A function \( f(x, y) \) is homogeneous of degree \( n \) if for any scalar \( \lambda \):

\[ f(\lambda x, \lambda y) = \lambda^n f(x, y) \]

For a differential equation to be homogeneous, the terms in the equation should be expressible in such a way that they can be scaled by a common factor.

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