# Find a PDE that satisfied by all the functions of the form

• Dec 25th 2010, 06:08 PM
dwsmith
Find a PDE that satisfied by all the functions of the form
Find a PDE that satisfied by all the functions of the form

$u=f(x^2-y^2)$

f can have as many derivatives as needed.

How would I go about doing this?

Thanks.
• Dec 25th 2010, 08:08 PM
Sudharaka
Quote:

Originally Posted by dwsmith
Find a PDE that satisfied by all the functions of the form

$u=f(x^2-y^2)$

f can have as many derivatives as needed.

How would I go about doing this?

Thanks.

Dear dwsmith,

$u=f(x^2-y^2)$

$\dfrac{\partial u}{\partial x}=2x\dfrac{\partial f}{\partial(x^2-y^2)}$

$\dfrac{\partial u}{\partial y}=-2y\dfrac{\partial f}{\partial(x^2-y^2)}$

Eliminate $\dfrac{\partial f}{\partial(x^2-y^2)}$ from these two equations and you will get the required partial differential equation.