I come across some problems, I'm working on finding Differential Equations for n-parameter Family of solutions. However the problem is constructing the n-parameter family equation to work with to find a Differential Equation for the particular n-parameter family equation. Here's the problem, Find a differential equation whose solution is 18. A family of circles of fixed radii and centers on the x axis. Now i know that a family of circles with center at origin is [tex] x^2 + y^2 = r^2, r > 0 [/tex] However I do not know how to form an equation such that a family of circles of fixed radii, centers on the x axis. I find that the fixed radii can be represented by a constant? The answer for 18 is [tex] (yy')^2 + y^2 = a^2 [/tex] That is the differential equation, however I do not know how to get the differential equation if I can't construct a family of circles of fixed radii that centers on the x axis. Here is another problem 19. A family of circles of variable radii, centers on the x axis and passing through the origin. There is only one problem such as problem 21 that gives the equation to you, so you don't have to construct it. 21. A family of circles with centers in the xy-plane and of variable radii. Then it gives a Hint: Write the equation of the family as [tex] x^2 + y^2 - 2c_1x - 2c_2y + 2c_3 = 0 [/tex] I read the problems, and I get an idea of what it wants but, the construction of an equation is difficult.