Which of the following is a homogeneous differential equation? (A) `(4x" "+" "6y" "+" "5)" "dy" "" "(3y" "+" "2x" "+" "4)" "dx" "=" "0` (B) `(x y)dx-(x^3+y^3)dy=0` (C) `(x^3+2y^2)dx+2x y""dy=0` (D) `y^2dx+(x^2-x y-y^2)dy=0`

Explanation

Correct answer is D.


We know the property of homogeneous differential equation i.e.


``
`frac{d y}{d x}=f(x, y)`


`Rightarrow f(lambda {x}, lambda {y})={f}({x}, {y})`


``
In the given set of options, addition of power is same throughout the equation.