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

MCQ

Which of the following is a homogeneous differnetial equation?

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

✓

Answer

Correct option: D.

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

A differential equation is said to be homogenous if all the in the terms in the equation have equal degree and it can be written in the from $\frac{\text{dy}}{\text{dx}}=\frac{\text{f}(\text{x,}\text{y})}{\text{g}(\text{x,}\text{y})}.$
In $(a), (b)$ and $(c),$ the degree of all the terms is not equal.
But in the equation $y^2 d x+\left(x^2-x y-y^2\right) d y=0,$ the degree of all the terms is $2.$
Thus$, (d)$ constant a homogeneous differential equation.

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