What is the solution of the differential equation
` (dy)/(dx) + sqrt((1-y^(2))/(1-x^(2))) = 0 ? `

Options

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

Answer

A

Explanation

The differential equation is
` (dy)/(dx) + sqrt((1-y^(2))/(1-x^(2)))=0`
` Rightarrow (dy)/(dx) =- sqrt((1-y^(2))/(1-x^(2)))`
` Rightarrow (dy)/(sqrt(1-y^(2)) = (-dx)/(sqrt(1-x^(2)))`
` int 1/(sqrt(1-y^(2))) dy = int 1/(sqrt(1-x^(2))) dx =0`
` Rightarrow sin ^(-1) y = sin^(-1) x=C`