Question

Which of the following is/are correct regarding homogeneous differential equation?

• A. Represented in the form: $M(x,y)dx-N(x,y)dy=0$
• B. Represented in the form: $M(x,y)dx+N(x,y)dy=0$
• C. Both $M(x,y),N(x,y)$ are homogeneous functions of the same degree
• D. $M(x,y),N(x,y)$ are homogeneous functions with different degrees

Answer 1

Answer: (B), (C)

Both $M(x,y),N(x,y)$ are homogeneous functions of the same degree
Represented in the form: $M(x,y)dx+N(x,y)dy=0$

a Differential equation of the form$M(x,y)dx+N(x,y)dy=0$ is called a homogenous differential equation if both $M(x,y)$ and $N(x,y)$ are homogenous and are of same degree $k$ where $kϵR^{+}$