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

Solution:

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

1-y^2=(x+c)^2

Hence the center of the circle lies on the x axis and the radius of the circle is 1.