The general solution of the differential equation `sqrt(1-x^(2)y^(2)) dx = y dx + x dy` is

Options

A. `sin(xy) = x + c`
B. `sin^(-1)(xy)+x = c`
C. `sin(x+c)=xy`
D. `sin(xy)+x = c`

Answer

C

Explanation

`sqrt(1-x^(2)y^(2))dx = y dx + x dy`
`rArr" "dx=(d(xy))/(sqrt(1-(xy)^(2)))`
`rArr" "x + c = sin^(-1)(xy)`
`rArr" "xy = sin (x + c)`