Well, the problem with that equation is that it is an implicit function and cannot be solved algebraically for either variable. (at least, I have not been able to do so yet

) I am not sure if this works, but it might be possible to treat it as a function of another variable, say something like z=f(x,y) and find a double integral with respect to x and y.
Does anyone know if there is a way to get integrals for implicit functions? (a chain rule for integrals maybe?)
There is something called Euler's method for solving equations of the form f(x,y)=dy/dx numerically, but that only give approximate results, and I like things to be precise.


Finding C once you have the antiderivative is pretty easy; you just find a point on the original equation, substitute it into the new one and solve for C. It is the antiderivative that's the hard part here.
