Consider a curve whose Cartesian equation is given by , and which passes through the origin. A rectangular region is drawn with one corner at the origin, and the other corner on the curve of the graph of . The curve then divides the rectangle into two pieces and . These two pieces of the rectangle then generate solids of revolution when rotated about the -axis. If the volume of one solid of revolution is always times the volume of the other solid of revolution, find the equation for .