Question

The solution of the differential equation y dx - x dy = xy dx is ______.

Options

• x² = e^x y²

• x = ye^x

• xy = e^x

• x²y² = log x

Answer 1

The solution of the differential equation y dx - x dy = xy dx is x = ye^x.

Explanation:

We have differential equation y dx - x dy = xy dx

`=> ("y" dx - x "dy")/"xy" = "dx"`

`=> "d"(log  x/"y") = "dx"`

On integrating both sides, we get

`log (x/y) = x => x/"y" = "e"^x`

⇒ x = ye^x