Hello,

This is a snippet from a book:

I am trying to apply the same principle to:

$\displaystyle x^2+(y-c)^2=1+c^2$

Rearranging:

$\displaystyle u(x,y)=\frac{x^2}{y}+y-\frac{1}{y}=2c$

Then:

$\displaystyle \frac{\partial v}{\partial y}=\frac{\partial u}{\partial x}=\frac{2x}{y}$

$\displaystyle \frac{\partial v}{\partial x}=-\frac{\partial u}{\partial y}=\frac{x^2}{y}-1-\frac{1}{y^2}$

But from another thread, a function that satisfies both partial derivatives cannot be found.

I don't know the best way to link to a another thread but here it is anyway:

I am wondering if using the Cauchy-Riemann equations for Orthogonal Trajectories doesn't work in general or if I am missing something?