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(dy)/(dx) = (xy+y)/(xy+x), then the solu...

`(dy)/(dx) = (xy+y)/(xy+x)`, then the solution of differential equation is

A

`x+y=log((cy)/(x))`

B

`x+y=log(cxy)`

C

`x-y=log((cx)/(y))`

D

`y-x=log((cx)/(y))`

Text Solution

Verified by Experts

The correct Answer is:
D
Given differential equation is
`implies((1+y))/(y)"dy"=((1+x))/(x)dx`
`impliesint((1)/(y)+1)dy=int((1)/(x)+1)dx`
`implieslogy+y=logx+x+logc`
`implies" "y-x=log((cx)/(y))`
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