Solving Difficult Problem: $\partial x/\partial y$ as Function of x

[redtree]

Given the following:

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

Solve for y as a function of x.

 

[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?

 

[redtree]

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?

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).

 

[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 across 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.

 

[redtree]

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 across 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.

Thanks. I look forward to it.