Question

The general solution of the differential equation `(ydx - xdy)/y` = 0

Options

• `xy = c`

• `x = cy^2`

• `y = cx`

• `y = cx^2`

Answer 1

`y = cx`

Explanation:

The differential equation is `(ydx - xdy)/y` = 0 or `dx - x/y  dy` = 0 or `(dx)/x - (dy)/y` = 0

Integrate we get,

`int (dx)/x - int (dy)/y = c^1` ⇒ `log x - log y = c^1` or `x/y = c^1`

Putting `c^1 = 1/c`

`x/y = 1/c, y = cx` is the require solution.