Find a PDE that satisfied by all the functions of the form
$\displaystyle u=f(x^2-y^2)$
f can have as many derivatives as needed.
How would I go about doing this?
Thanks.
Dear dwsmith,
$\displaystyle u=f(x^2-y^2)$
$\displaystyle \dfrac{\partial u}{\partial x}=2x\dfrac{\partial f}{\partial(x^2-y^2)}$
$\displaystyle \dfrac{\partial u}{\partial y}=-2y\dfrac{\partial f}{\partial(x^2-y^2)}$
Eliminate $\displaystyle \dfrac{\partial f}{\partial(x^2-y^2)}$ from these two equations and you will get the required partial differential equation.