#### Question

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

#### Solution

Function F(*x*, *y*) is said to be the homogenous function of degree *n,* if

F(λ*x*, λ*y*) = λ^{n} F(*x*, *y*) for any non-zero constant (λ).

Consider the equation given in alternativeD:

Hence, the differential equation given in alternative **D** is a homogenous equation.

Is there an error in this question or solution?

Solution Which of the Following is a Homogeneous Differential Equation? Concept: Methods of Solving First Order, First Degree Differential Equations - Homogeneous Differential Equations.