Question

The solution for the differential equation `("d"y)/y +("d"x)/x` = 0 is ______.

Options

• `log x * log y` = c

• x + y = c

• `1/y + 1/x` = c

• xy = c

Answer 1

The solution for the differential equation `("d"y)/y +("d"x)/x` = 0 is xy = c.

Explanation:

`("d"y)/y +("d"x)/x` = 0

Integrating on both sides, we get

`log x + log y = log c`

⇒ `log(xy) = log c`

⇒ xy = c