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 ydy=0` (D) `y^2dx+(x^2+x y-y^2)dy=0`

Explanation

A) `(4x+6y+5)dy+(3y+2x+4)dx=0`

`M(x)=4x+6y+5`

`N(x)=3y+2x+4`

If we put `x=2x,y=2y`

`M(2x,2y)=z(4x+6y)+5`

`N(2x,2y)=z(3y+2x)+4`

`M(2x,2y)`

`=z^nM(x,y)N(2x,2y)`

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