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 these

Answer

C

Explanation

Given differential equation is
`(dy)/(dx)=(x-y+3)/(2(x-y)+5)`
Put `x-y=v`
`implies(dy)/(dx)=1-(dv)/(dx)`
`:.1-(dv)/(dx)=(v+3)/(2v+5)`
`implies (dv)/(dx)=(v+2)/(2v+5)`
`implies int(2+1/(v+2))dv=intdx`
`implies 2v+log(v+2)=x+c`
`implies2(x-y)+log(x-y+2)=x+c`