`(1 + xy) ydx + (1-xy)xdy = 0`

Options

A. `(x)/(y)+(1)/(xy)=k`
B. `log((x)/(y))=(1)/(xy)+k`
C. `(x)/(y)+(1)/(xy)=k`
D. `log((x)/(y))= xy + k`

Answer

C

Explanation

`y dx + x dy + xy^(2) dx - x^(2) y dy = 0`
`rArr" "(y dx + x dy)/(x^(2)y^(2))+(dx)/(x)-(dy)/(y)=0`
On integrating, we get
`-(1)/(xy)+log x - log y = k rArr "log"(x)/(y)=(1)/(xy)+k`