Which of the following is a homogeneous differential equation? - Vidyadip

MCQ

Which of the following is a homogeneous differential equation?

A
$ (4 x+6 y+5) d y-(3 y+2 x+4) d x=0 $
B
$(x y) d x-\left(x^3+y^3\right) d y=0 $
C
$ \left(x^3+2 y^2\right) d x+2 x y\ \ d y=0 $
✓
$ y^2 d x+\left(x^2-x y-y^2\right) d y=0 $

✓

Answer

Correct option: D.

$ y^2 d x+\left(x^2-x y-y^2\right) d y=0 $

Out of the given four options, option $(D)$ is the only option in which all coefficients of $dx$ and $dy$ are of same degree i.e., $2$. It may be noted that $xy$ is a term of second degree.
Hence differential equation in option $(D)$ is Homogeneous differential equation.

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