The solution of the differential equation `(dy)/(dx)-1=e^(x-y),` is a. `(x+y)e^(x+y)=0` b. `(x+C)e^(x+y)=0` c. `e^{-(x-y)}=x+c` d. `(x-C)e^(x+y)+1=0`

Explanation

Answer is C

`frac{d y}{d x}-1=e^{x-y} `


`Rightarrow d y-d x=e^{x-y} cdot d x `


`Rightarrow frac{-d(x-y)}{e^{x-y}}=d x `


`Rightarrow d x+e^{-(x-y)} cdot d(x-y)=0 `


`Rightarrow x-e^{-(x-y)}=c, `

`e^{-(x-y)}=x+c`