For the differential equation $(x + y)dy + (x − y)dx = 0$, which of the following is/are correct?

(A) Differential equation is homogeneous
(B) Order of differential equation is 1
(C) Integrating factor of differential equation is $e^x$
(D) Degree of the equation is not defined

Choose the correct answer from the options given below:

(A) and (B) only

The correct answer is Option (4) → (A) and (B) only

Given:

$(x+y)\,dy + (x-y)\,dx = 0$

(A) Differential equation is homogeneous:

Both $x-y$ and $x+y$ are of degree $1$.

(A) true

(B) Order of differential equation is $1$:

Only $\frac{dy}{dx}$ occurs after rearranging.

(B) true

(C) Integrating factor is $e^{x}$:

The equation is homogeneous and solved by substitution $y=vx$. Integrating factor does not appear.

(C) false

(D) Degree of the equation:

Highest power of $\frac{dy}{dx}$ is $1$, so degree is defined.

(D) false

Correct statements: A and B