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:
Answer & explanation
Correct answer: option 4
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