Re: Help solving equation

On Feb 13, 12:13 pm, David Rutherford <drutherf...@xxxxxxxxxxx> wrote:
I have an equation I'm trying to solve for the function f(x,y). The
equation is

df = (ydx - xdy)/((x^2 - y^2)^{1/2})

Any help would be muchly appreciated.

Thanks,
Dave

If you mean that the partial derivatives are @f/@x = y/sqrt(x^2-y^2)
and @f/@y = -x/sqrt(x^2-y^2), then there is no such function. You need
@^2f/@y@x = @^2f/@x@y, so you would need (@/@y)(y/sqrt(x^2-y^2)) [=
x^2/(x^2-y^2)^(3/2)] equal to (@/@x)(-x/sqrt(x^2-y^2)) [= y^2/(x^2-y^2)
^(3/2)]. Therefore, except on the lines x^2 = y^2 we do not have the
required equality.

R.G. Vickson
.

Quantcast