what is the solution of the differential equation
`(dy)/(dx)=e^(x-y) (e^(y-x) -e^(y))` ?

Options

A. `y=x-e^(x) +c`
B. `y =x+e^(x)+c`
C. `y=3^(x-y)-e^(y)+c`
D. none of these

Answer

A

Explanation

Given differential equation is
` (dy)/(dx) = e^(x-y) (e^(y-x) -e^(y)) = e^(-y) .e^(y) (e^(x) e^(-x) - r^(x))`
` Rightarrow int1dy = int (1-e^(x)) dx`
` Rightarrow y =x -e^(x) +c`