The solution of `(1+x)(dy)/(dx)+1=e^(x-y)` is

Options

A. `e^(y)(x+1)=c`
B. `e^(y)(x+1)=e^(x)+c`
C. `e^(y)(x+1)=ce^(x)`
D. `(x+1)=e^(x)+c`

Answer

B

Explanation

`(x+1)(dy)/(dx)+1=(e^(x))/(e^(y))`
`rArr" "e^(y)(x+1)(dy)/(dx)+e^(y)=e^(x)`
`" "int(d)/(dx)(e^(y)(x+1))dx = int e^(x) dx`
`rArr" "e^(y)(x+1)=e^(x)+c`