The soluiton of the differential equation `y dx- x dy = xy dx` is ……

Options

A. `x^(2) = e^(x) y^(2)`
B. `x = ye^(x)`
C. `xy = e^(x)`
D. ` x^(2)y^(2) = log x`

Answer

B

Explanation

We have different equation `ydx - xydx = xydx`
`rArr " "(ydx - xdy)/(xy) = dx`
`rArr " "d(log .(x)/(Y)) = dx`
On intergating both sides, we get
`log ((x)/(y)) = rArr x rArr (x)/(y) = e^(x)`