Question

The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.

Options

• xy = C

• x = Cy²

• y = Cx

• y = Cx²

Answer 1

The general solution of the differential equation `(y dx - x dy)/y = 0` is y = Cx.

Explanation:

Given the differential equation

`(y dx - x dy)/y = 0`

or `dx - y/x dy = 0`

and  `dx/x - dy/y = 0`

On integrating,

⇒ log |x| - log |y| = log |C'|

⇒ `log |x/y| = log |C'|`

⇒ `x/y = C'`

⇒ `y = 1/C' x`

⇒ y = Cx

Where `1/C = C`

Which is the required solution.