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

Options

A. ` y = (x+2)+Ce^(x)`
B. `y=-(x+2)+Ce^(x)`
C. `x=-(y+2)+Ce^(y)`
D. `x=(y+2)^(2)+Ce^(y)`

Answer

c

Explanation

Given , `(dx)/(dy) = x+y+1`
` rArr (dx)/(dy) - x = y +1`
` :. IF = e^(int-1dy) = e^(-y)`
Its solution is given by
` x . IF = int IF xx Q dy + C`
` rArr x * e^(-y) = int (y+1)e^(-y) + int e^(-y) dy + C`
` rArr xe^(-y) = - (y+1) e^(-y) -e^(-y) +C`
` rArr xe^(-y) = - (y+1) e^(-y) -e^(-y) +C`
` rArr x = - (y+2) +Ce^(y)`