The solution of ` (dy)/(dx) = sqrt(1-x^(2)-y^(2)+x^(2)y^(2))` is
Where c is an arbitrary constant.

Options

A. `sin ^(-1)y = sin^(-1) x +c`
B. ` 2 sin^(-1) y = sqrt(1-x^(2))+sin^(-1) x +c`
C. ` 2sin^(-1)y = x sqrt(1-x^(2)) +sin^(-1) x+c`
D. `2 sin^(-1) y =x sqrt(1 -x^(2))+cos^(-1) +c`

Answer

C

Explanation

` (dy)/(dx) = sqrt(1 -x^(2) -y^(2) +x^(2)y^(2))`
` (dy)/(dx) = sqrt ((1 -x^(2)) (1-y^(2)))`
`Rightarrow (dy)/(sqrt(1-y^(2))) = sqrt(1-x^(2))`.dx
` = int (dy)/(sqrt(1-y^(2)))= int (sqrt(1-x^(2))).dx`
`sin^(-1) (y/1) = x/2 sqrt(1-x^(2)) + 1/2 sin^(-1) (x/1)+c`
` sin^(-1) y=x sqrt(1-x^(2))+sin^(-1) x +c`