Which of the following is a homogeneous differential equation?
(a) (4x + 6y + 5) dy − (3y + 2x + 4) dx = 0
(b) xy dx − (x ³ + y ³) dy = 0
(c) (x ³ + 2y ²) dx + 2xy dy = 0
(d) y ² dx + (x ² − xy − y ²) dy = 0

(d) y² dx + (x² − xy − y²) dy = 0

A differential equation is said to be homogenous if all the terms in the equation have equal degree and it can be written in the form $\frac{dy}{dx}=\frac{f\left(x, y\right)}{g\left(x, y\right)}$.

In (a), (b) and (c), the degree of all the terms is not equal.
But in the equation y² dx + (x² − xy − y²) dy = 0, the degree of all the terms is 2.
Thus, (d) contains a homogeneous differential equation.