The differential equation !!(dy)/(dx) = sqrt(1-y^2)/y!! determines a family of circles with:
- Variable radii and a fixed centre at !!(0,1)!!
- Variable radii and a fixed centre at !!(0,-1)!!
- Fixed radius 1 and a variable centres along !!y-axis!!
- Fixed radius 1 and a variable centres along !!x-axis!!
We need to integrate the given differential equation and find the equation of the graph which will satisfy the given equation.
So we have !!ydy/(sqrt(1-y^2)) = dx!!
Now you could see that the differential of !!y^2!! is !!2y!!.
So we get !!-sqrt(1-y^2)=x+c!!
Hence the center of the circle lies on the x axis and the radius of the circle is 1.