The solution of the differential equation `(dy)/(dx)=(x-y+3)/(2x(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)`
Let `x-y= v rArr (dy)/(dx)=1-(dv)/(dx)`
`(dv)/(dx)=(v+2)/(2v+5)`
`rArr int (2v+5)/(v+2) dv =int dx`
`rArr int (2+(1)/(v+2))dv= int dx`
`rArr 2v + log (v+2) =x+c`
`rArr (2x-y)+log (x-y+2)=x+c`