The solution 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)=logx`.

Answer

B

Explanation

We have differential equation `ydx-xdy=xydx`
`implies(ydx-xdy)/(xy)=dximpliesd("log"(x)/(y))=dx`
On integrating both sides, we get
`log((x)/(y))=x implies(x)/(y)=e^(x)impliesx=ye^(x)`