# Difficult problem

1. Jun 22, 2008

### redtree

Given the following:

$$\partial x$$/$$\partial y$$ = A * [B/y + C/(y-D)]^(1/2)

Solve for y as a function of x.

2. Jun 22, 2008

### DeaconJohn

Replacing the partial of x with respect to y with dx/dy, and moving the dy from the denominator of the l.h.s. to the numerator of the r.h.s., and then taking the indefinite integral of both sides, does not that express x in terms of an (incomplete) elliptic integral of y?

3. Jun 22, 2008

### redtree

Solving for x as a function of y is easy. It's just as you suggested. The hard part is solving for y as a function of x (at least for me).

4. Jun 22, 2008

### DeaconJohn

Well, if it is an elliptic integral like I suspect, then that is a classic and difficult problem. Many very good mathematicians were unable to make any progress on it for many years. However, there is now a known method of solving it. That is, if I remember correctly. In any case, it's the kind of stuff Ramanujan was good at. I post a reference next time I run accross one.

Nobody said mathematics was easy. Many elementary things are beyond our current grasp. Mathematicians don't even understand which integers in cyclotomic fields are units. It's because there are a lot of hard problems.

5. Jun 23, 2008

### redtree

Thanks. I look forward to it.