Question

Find the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`

Answer 1

`dy/dx + sqrt((1 - y^2)/(1 - x^2)) = 0`

`=> dy/dx = - sqrt((1 - y^2)/(1 - x^2))`

`dy/sqrt(1 - y^2) + dx/sqrt(1 - x^2) = 0`

On integrating

sin^-1 y  + sin^-1 x = C

which is the required solution.