The solution of the differential equation
`(dy)/(dx) = (x-y+3)/(2(x-y)+5)` is

Options

A. `2(x-y)+log (x-y)=x+C`
B. `2(x-y)-log(x-y+2)=x+C`
C. `2(x-y)+log(x-y+2)=x+C`
D. None of the above

Answer

c

Explanation

Given differential equation is
` (dy)/(dx) = (x-y+3)/(2(x-y)+5)`
Put ` x - y = v rArr (dy)/(Dx) = 1- (dv)/(dx)`
` :. 1 - (dv)/(dx) = (v+3)/(v+5) rArr (dv)/(dx) = (v+2) /(2v+5)`
` rArr int (2+ 1/(v+2)) dv = int dx`
` rArr 2(x-y) + log (x-y+2) = x+C`